The name core is misleading. Playing a core definitely does NOT make you the most significant force in the game, however at your stage in the game (lets assume that stage is late game, this IS 6.82) you will become much more influental than other roles.

Many cores are very weak early game, bringing little or nothing to the table in terms of claiming early objectives, getting kills or MAKING SPACE TO FARM. This guide is much more relevant since 6.82, and that is why i have decided to write it now, as most teams will aim to out-carry each other, and as such their goals will include quite high on the list; creating space for higher farm-priority heroes, and farming for levels and exp.

A few misconceptions.
1. All cores/ carries are right click heroes.
2. Cores are easier to play than supports (they may get more kills at times, but doesnt make them any easier to play).
3. Roaming and getting kills early is an effective way of obtaining gold.
4. The focus of every core is to become strong enough to get kills once fat enough.
5. Every core does best late game.

Why these things are will be explained throughout the guide.

First things first, lets try to explain what a 'core' is and when they are best suited.

Cores or carries are heroes that are given priority for gold, exp or both. Even Queen of Pain or often Jakiro are cores.

BUT, you there, you 2k scrub, this does not mean you build desolator on Jakiro or maelstrom on Queen of Pain. GOT IT? (BTW, I know the early pushing/ teamfight core meta is dead.)

Ok. A core can snowball with experience or gold. Carries that utilise gold primarily are much more commonly seen as it doesnt cap off so early, allowing better late game transitioning, but most cores can utilise both very well.

Leshrac is a good example.

While he is often played as a support, he can be played as a core in a way very reminiscent of Death Prophet. His farm rate AND kill potential increase significantly with levels. With tankability and the mana pool and regen to go with it, he deals incredible amounts of damage in a teamfight and has pushing power that could put a NP to shame.

But dont all heroes need levels? How are the supports supposed to stay levelled enough?
The thing is, most supports should be and are often picked because of what they can bring to the table in terms of their abilities. Rarely is a position 4 or 5 (4th or 5th farm priority, eg takes no farm, stacks for others, pulls creeps for most of their EXP) support picked purely for damage. As can be seen with most abilities, the stun/ slow/ any other utility effects often scale much differently to a nuke. As a result, most good supports dont utilise the EXP as much as, say, a Zeus or Death Prophet would.

While between 1/2 and 3/4 of all heroes can be played as cores, this doesnt mean they should. Use your disgression. Unless you know how to play Warlock core, dont do it. It makes you look really stupid. If you are unsure what is a carry and what isnt, stick to the basic right clicking ones.

Just a reminder that in a pub game, things like Leshrac core are harder to pull off and rarely seen. Just because a hero can carry or play a core role, doesnt mean they should. Play them according to what your draft is like. A carry that takes alot of farm away such as Natures Prophet or a Naga Siren going the radiance build makes it hard to play someone that is heavily reliant on farm. No more than 3 cores should ever be picked. THE 5 CORE TEAM DOESNT WORK! In the cases where your team has the full three cores, they should not all be super-farming-late-game-cores such as Anti-Mage. In fact, try to never even draft 2 heroes that require intensive farming or tend to take alot of farm like Meepo can do and Natures Prophet does. Dont be that ♥♥♥♥♥♥♥ who refuses to play anything but core, and then last picks a Morphling when you already have Alchemist, Anti-Mage and Death Prophet.

What this means is dont play KOTL core. Just dont. Really if thats the only thing you get out of this guide, i will still be happy.

This section is aimed at heroes that dont spend the entire early game farming, or those interested as to what constitutes space being created and available.

Creating space isnt hard. While many would not have heard of this 'Space', many do it by accident and some heroes make space just by existing.

Space refers to the availability of time and map control. If you are not pressuring the other team, they may decide to attempt to stop the cores' farm directly, and they can more easily intervene if the core decides to farm a lane or an unprotected jungle (ward the entrances to the jungle in order to 'secure' it) or even try to sneak a tower. If 4 of your team are forcing the midlane tier 2, the choice the other team face is to either disrupt the position 1's farm a little, or to try to defend this tower that represents a large amount of map that they are losing control of. Guess what, 9 times out of ten the decision will be to defend, meaning the carry can free farm.

Space can be created simply by having wards on the map securing key farming areas. It's that simple to pick up, so much harder to master. Knowing how and when to create space for cores comes with experience in my opinion. If you want to win games as a support, learn to make space.

If you want to learn more about this, play with friends more, learn how to ward better. Communicate even, as radical as it may seem.

Technically sitting in lane while the carry does the same DOES secure his farm, but i mean really, just place a ward to help them and carry teleport scrolls in case they get dived on. That way you can do other support stuff. Like roaming/ganking and stacking jungle camps.

Farming patterns are for those devoted enough, but not experienced enough to know where and when to farm at any given occasion. If you play one core alot, draw a farming patten on a map. Maybe make multiple, just never stick to the same pattern in every game. If you dont have map control of a certain area that you plan to farm in alot, you could easily die.

Here is a map. Put some thought into where is safe to farm when, im not going to tell you everything about every situation.

Some advice: DONT SIT IN LANE.
Got it?

Even in the first 10 mins of the game, if you are getting free farm a good way to maximise your GPM is by quickly clearing creep waves (always do this when you are mid, it gives you time to collect runes or farm the jungle) and clearing a jungle camp, or stacking, just do anything that achieves something in that time before the next creep wave. Even if you cant kill the camp completely (happens often in dire safelane where closest camp is the hard camp), deal some damage so they can be cleared later. Leaving lane creeps unfarmed in the early-game is a sin. Kill them all (often I leave cataplaults), them move on, leaving no gold or EXP to waste.

Carry TPs

When you are having troubles farming in your position, it can be beneficial to rotate lanes (or even switch to jungling primarily. Do this early only if things are bad in lane.), and just walking wastes time. Time is money as a carry, but dont be too afraid to relocate to somewhere where farming will be easier going, so long as you dont waste too much time in transport. Also TPs allow you to
1. Avoid a gank you can see incoming.
2. JUUUKKKKESS
3. Help defend a tower
4. Help push a tower
5. Go back to base for regen (only do this often as heroes like Ember Spirit, Morphling and Meepo as they can quickly return)
6. Help a teammate being dived on
7. Prepare for a gank

About that last point...

Think about it, how much gold do you actually get from a kill early on. 250? 450? Not much, isnt it. In a minute gank, you could instead kill 2 entire creep waves (400 gold) and farm a jungle camp (75 up to ~250). While those farming amounts are best case scenarios, it isnt hard to get 80% of the maximum amount consistantly with a little practice.
Anyway, TPing into a lane is obvious and rarely works unless the other team wants to fight.

Also, DONT WASTE TIME. If you are a very late game oriented core, dont roam, just farm. Stay completely tunnel-visioned. If you are a Puck (yes he is a core as he is normally played, dont think that means you can take all the farm. Puck is the kind of core that does well position 3 or 2) dont sit in lane last hitting. You dont really need gold to be relevant as many cores, so it is viable to go earn kills. Kills create space and give decent gold overall. As mentioned before, in terms of personal gain only, farming gives more than kills do early on, but te benefit to your team cannot be overlooked when playing a core with farm priority number 2 or 3.

This guide could be considered complete, but there is still more i would like to add. If you have any ideas as to what you want to see here, post a comment saying so. Remember when criticising, you may not necessarily be right.