Very short summary:

Build construction sectors, logging camps, iron mines, steel mills for your GDP growth to take off. Then only build stuff that the private investors can't (like universities and armies) or if you have a goods shortage.

To get off serfdom: Force spawn a peasants movement by taxing grain, remove the tax again, boost the peasants movement, make the landowners happy with local police force, then start enacting homesteading, cancel it, now you can enact tenant farming easily. Now go get interventionism, and if you can't then get agrarianism until you can.

To destroy landowners: piss off the lower class as much as possible with high taxes and tax every basic good until a revolution starts, then abdicate your king. You will get an event for -100% landowners clout for 5 years. Use this time to get voting rights, free speech and parliament.

Your infamy is a resource, always go around the world and subjugate nations. Infantry+artillery armies to fight large fronts, pure infantry to defend coasts, infantry+cavalry for sneaky naval invasions. Destroy great powers by forcing them to sell all their grain and other food to you in war goal treaties.

Power block: Sovereign empire is best, if you can't get it then trade league. Mandates: construction, food, colonies, vassalisation, foreign investments.

Pops are your most imporant resource. Boost birth rates with legal guardian law, food company, food mandate, happy religious IG, and SoL between 10-20. Boost migration with No migration controls, multiculturalism, and outlawed slavery.

TLDR:

1. Only build construction sectors, construction materials buildings and government stuff (barracks, admin, universities). Let the capitalists handle the rest to make them stronger over time.
2. Use companies to boost throughput of your construction sector, which boosts GDP growth.
3. Get off serfdom, traditionalism and isolationism
4. Plenty of railroads, ports and trade centers
5. Use gold always PMs, purple PMs when profitable, and green PMs when no peasants.
6. Grant Foreign investment rights if you got millions of peasants, get foreign investment rights if not
7. Education = qualifications = hiring


1) Avoid government construction

Your construction capacity is shared between the government and the private sector. So when you build stuff, the private investors can build less. This greatly hampers their growth. Its also bad that they now have to compete with government owned buildings.

Ideally you just want to build:

• New construction sectors
  
• Buildings to lower cost of construction (logging camps, iron mines, steel mills)
  
• Government stuff (admin, army, universities)

Check the private investment pool on the construction screen. If its growing, it means you have too few construction sectors. If its at zero it means all private capital has been spent, and then its okay to make some more government owned buildings.

2) Throughput is key

Profitability is key to growing fast, and to be profitable you want high throughput. Boost it by:

• Companies! The company boosts its own buildings with Company throughput boost, but can also boost other buildings with either its prosperity bonus or prestige goods. This means anything with prestige boosts like the tool or steel company are very good. You almost always want the tooling company and the steel company.
  
• Use decrees. These are often forgotten but can give a massive boost
  
• Completing journal entries, then pick the bonus that gives output, NOT the one giving tech progress.

3) Get the right laws

You want to get off serfdom, isolation and traditionalism ASAP. Do this quickly by:

• To get off Serfdom, wait for a peasants movement to spawn, then boost it. They will support Homesteading which you probably can't pass due to stall chance. But if you start enacting it and then cancel it, the Peasants movement will now support Tenant Farmers. If the Landowners give Tenant Farmers too much stall chance, make them happy by passing Local Police or another law they like.
  
• If you have Isolationism as an unrecognized country, you can often get off it by starting a humiliation play against a great power like Great Britain. They will often add Open Market as their war goal. Then just press Back Down to get Free Trade. If this is not an option, then just live with isolationism until you can pass any other trade law naturally. Isolationism does have the benefit that no one will buy your construction goods, so wood/iron/steel can get very cheap.
  
• As soon as you get off Serfdom you can often pass Interventionism just after. If it doesn't have support then Agrarianism usually does, and its also better than Traditionalism.
  
• Passing landed or especially wealth voting helps move power away from the Landowner aristocrats and over to the Industrialist capitalists, which will allow you to pass better economy laws. Don't pass Census or Universal suffrage early, that just gives all the power to the peasants.

4) Create proper infrastructure

You want to have enough Railroads, Trade Centers and Ports.

• For railroads just press them on the building Lens and sort by infrastructure. If any state has negative infrastructure build railroads. You might need to subsidize your railroads. Having your farms use Rail Transport production method boosts their profitability so you don't have to subsidize too much.
  
• For Trade Centers just build enough so there is excess Trade Capacity and no unused trade potentials.
  
• For ports make sure you have enough convoys to support your trade centers and enough convoys so you don't go negative when you move soldiers around during wars.

5) Use the right production methods

The gold ones are always better, if it shows that profitability will decrease then its just because it requires a new resource you aren't making enough of, but now demand will be created and your capitalists will start creating that building and your trade centers will buy it from the world market.

The purple ones depends on the current market, for textile and furniture factories there's often high demand for the basic goods and low demand for the luxury goods. It also requires silk which you might not be able to get.

The labor savings ones are almost always bad and should only be used to get more free workers if you have run out of them, or in the case of using Rail Transport to make railways profitable.

6) Foreign investments

Remember:
The country constructing the buildings will own those buildings, and extract the profits. The country that receives the buildings will get jobs for their peasants and goods on their market, boosting their GDP.

If you start as a backwards nations it can be a very good idea to offer investment rights into your country to everyone. If you are a nation like China or Sokoto you will have millions of peasants that needs to get into jobs ASAP. Investment rights means suddenly you have many western nations adding jobs and goods to your country which boosts your GDP by a ton. But your own capitalists wont get much richer.

When you become or start as a nation with few peasants its best to own as many buildings as possible, as its a great way to create wealthy capitalists. Nationalise your own country's buildings, then try and get foreign investment rights. Remember to give your companies Investment Rights charter, so they will make Regional HQs.

7) Qualifications

If you get the warning that you don't have enough qualifications for a new building or production method, you need to boost your qualification gain. Every week your population groups get new qualifications, the rate is determined by their literacy and any boosts to qualification rate such as decrees and universities. Its therefor a good idea to get high literacy (but not so high their minimum SoL becomes too high), and to build universities and enact education decrees in important states.

Conclusion

This covers 99% of cases. Sometimes you might need to create some buildings manually, such as if you have a very large deficit of a resource or railroads in a state, and sometimes you might need to subsidize your military goods buildings to keep them open in peacetime.

TLDR:

1. Piss off peasants so they revolution, then abdicate to destroy the Landowners IG and pass landed/wealth voting, Appointed Bureaucrats, Parliament, and Guaranteed Liberties. (and your economy laws from earlier)
2. Don't pass Census Suffrage or Universal Suffrage while you have tons of peasants and labourers.
3. End with Single Party State.
4. Use Agitators, political movements and generals to get the right laws and IG group leaders.
5. Culture laws gives tons of migration. Conquer a state in china to get multiculturalism.
6. No migration controls + tons of infrastructure + big market = tons of migration from other market members.


General tips

Use the Agitator and Political Movements mechanics fully. By that I mean boost political movements you like and supress the ones you don't like. This affects law passing chances, but also which trait new interest group leaders get. Go to the interest group to see the chances for new traits, then reroll bad leaders by exiling them. Check also the interest group AND trait of new generals before you hire them. A leader with a bad interest group (Landowner) but good trait (Reformer, Radical, etc) is worth gold as they can be made leader of their IG.

Power Structure

You almost always want to get off Monarchy and Autocracy, as the Landowners don't support laws that are good for your economy (Serfdom + Traditionalism). The usual route is to pass Landed Voting which usually isn't too hard and kills a lot of Landowner power, and then later on Wealth Voting which is even worse for the Landowners.

You do NOT want to pass Census Suffrage of Universal Suffrage early, as all the peasants and labourers vote for the farmers IG. But these laws are often needed to get from Monarchy to Parliament. And if you stay on Monarchy too long your Legitimacy will suffer.

Parliament means almost all governments are highly legitimate, and that means you can easily pass any law you like. So its a goal to get that eventually.

Appointed Bureaucrats is super strong as nations like Qing, because you gain free taxation capacity. Elected Bureaucrats also gives too much powers to the Petit Bougies.

Guaranteed liberties is also very strong.

You want to end with Single Party state, as its the ultimate choice to pass any law you want late game.

Usual route:

• Landed Voting
  
• Appointed Bureaucrats
  
• Guranteed liberties
  
• Wealth Voting
  
• Long wait
  
• Census Suffrage
  
• Parliament
  
• Universal Suffrage
  
• Single Party State

A little trick is to deliberately piss off the peasants so they start a revolution (try to pass consumption taxes and such). This allows you to right click on your monarch and click "Abdicate". This then fires an event that gives a massive -100% clout for Landowners.

State Religion is very bad as you can only have Religious Schools. Try to get Freedom of Conscious or Total Separation when possible. The Religious IG usually drops off in power by itself over time.

You almost always want the most inclusive culture law you can pass, it gives you migration attraction and keeps the minorities from revolting. You can get Cultural Exclusion or even Multiculturalism by conquering a full state in China and then waiting for a Minority Rights political movement to spawn.

Economy

Mostly covered in the Economy Section earlier. For taxes just pick whatever gives the most money.

Social

Legal Guardian is super strong due to its birth rate boost, so I keep this, though many players prefer Women's Rights due to the higher workforce. If you can get a high immigration (good culture laws, big market) early then you can live without the extra birth rate and pick Women's Rights.

Protected speech makes people happy but takes away your ability to boost and supress political movements, so I never go this far.

Always go for No Migration Control so you can get immigrants. With good SoL and culture law you will become a strong migration target. A good strategy is to join or create a large market, and then construct a ton of railroads, as local market migration attraction is boosted by the amount of unused infrastructure in a state.

TLDR:

1. Make armies of full infantry for defending your coasts, armies of 50/50 infantry/artillery for attacking, and armies of 50/50 infantry/cavalry for sneaky naval invasions.
2. Declare meaningless rivalries for free diplo points, use those points to keep vassals happy.
3. Make a power block to get good boosts and subjugate nations.
4. Destroy rivals with food transfer War Goal.
5. "Spend" infamy on small puppets around the world.

War

You basically want to have 3 army types:

• Armies of pure infantry to defend your coast against naval invasions. Infantry has the highest defence. It doesn't have to be many troops as the AI isn't good at naval invasions.
  
• Armies of 50/50 infantry and artillery to attack. Artillery has the highest offence but you get penalties if you have more artillery and infantry.
  
• Finally armies of 50/50 infantry and cavalry for naval invasions. This is because cavalry has higher occupation speed than anything else, so if you create sneaky naval invasions you can take a ton of land before the AI can respond.

Remember to use special orders for your generals (pillage is good for attack, adamant defence for defending) and mobilisation options. You can easily 2x your base unit stats with all the modifier boosts the game has.

Diplomacy

Directly conquering lands is rarely worth it in Victoria 3, instead you want to get puppets and colonies. From the very start of the game until the end, you want to be puppeting nations around the world, especially in South America, Africa and Southeast Asia, and creating colonies as soon as you get medicine against malaria. Your Infamy is a resource that is wasted if its at zero.

For bigger nations like China, you can often conquer states and then release some Chinese warlords as vassals.

Colonial mandate for your Power Block is a great way to keep infamy low and create colonies faster.

Remember to improve relations and fund lobbies to keep them loyal. If you lack diplo points just rival someone that doesn't matter, or any actual rival you forgot to formally rival. If they keep getting invaded during wars then just enact "Exempt from Service", this also makes them happier.

Puppets grant you income, workers and resources for your capitalists to use, and migration. To really abuse this you want to create a Power Block.

The best type of Power Block is a Sovereign Empire, only available to Monarchies. Pick the Mandate that gives you 20 authority per vassal, this means you get a ton of authority to spend on taxes, decrees and companies. You can also vassalize power block members for free. Other strong picks:

(I don't remember their actual names)

• Food industry, for birth rate
  
• Investment rights, for higher economic dependence. Makes vassals more loyal and it easier to get new power block members.
  
• Construction, to boost construction rate which boosts GDP growth.

How do you beat your rivals? The best dirty trick is to add a Wargoal to have them transfer food to you. Stuff like 90% of their grain for 5 years. This will create a nationwide famine for them. 1-2 of these war goals getting enforced in separate wars will kill off any empire.