Money in Mount and Blade Warband was typically easy to acquire via bandit hunting and slave trading. Once money was acquired it could be invested in gear and troops to fight stronger and more valuable bandits, or into businesses so that eventually you could focus on war over money grinding.

In WFAS the bandits barely give any money, with their guns your troops have a high mortality rate and you will frequently be KOd if you get in the thick of it without top tier armour, equipment is about 5x more expensive than in Warband, slaves are difficult to capture and worth very little, villagers are packing heat so raiding just isnt worth it, and businesses no longer exist

Trade is about as effective at making money as before, except for powder trading which feels like an exploit. Caravans are a new addition which were amazing at first but since have been nerfed into uselessness. Many guides will recommend caravans but they're all pre-nerf.

In Warband taxes from fiefs were usually considerably less than the cost of the garrisons. The main point was to store troops for military campaigns and villages were a more lucrative source of tax income, though even then they gave very little. They give a LOT more money in WFAS, and once you deduct troop wages for the garrison you'll still make about as much in taxes from a prosperous town as you could from 20 silk businesses in Native. They're really worth it this time, it's just getting to that stage that can be difficult.

While businesses are gone, you can now store money in banks to generate interest. This is at a rate of 14% per week. Since silk businesses cost 10k to start up and gave approx 500 per week in Warband this means the banks are about 3x more effective than businesses were. So if you can generate a few hundred thousand and bank it then you can rely on the interest to fund your campaigns, and with 1mil in the bank can buy special equipment for yourself and your companions and soldiers!

The main ways of generating money that will be covered in each section are:
1) Trade - Same deal as Warband but I will list the price margins of each item
2) Powder - This trade good is special and by far the most effective means of early money making
3) Taxes - About 20x higher than in Warband! I'll walk you through how to get a nice town fast and protect it for 20,000 in takes per week (after some investment)
4) Interest - If you can get to the point where your weekly interest excedes your spending then you have effectively infinite money

As an extra note: I recommend that after you've saved a bit of money you pick up a low level companion. Do some caravan escort quests to level them up a bit and give them charisma/trade. 3-4 trade is fine and will greatly increases your profits. If bandits attack your caravan dont bother trying to defend it, just go get another quest. You can defend the caravans but you'll need some good soldiers which costs money in recruitment, training and gear that your probably dont have at such an early point, and you shouldnt have to do that many just to get the first few levels on a lvl 1 companion anyway

Average price for goods at 0 trade. Buy goods for less than this price and sell them for more!

Oil: 400
Salt: 220
Linen: 180
Fish: 50
Beer: 100
Wool Cloth: 240
Flour: 50
Spice: 800
Velvet: 950
Wine: 200
Dried Meat: 70
Iron: 220
Dyes: 180
Bread: 30
Leather: 180
Pottery: 90
Hemp: 140
Tools: 400
Vodka: 300

All you need to do is find a town that sells large quantities of an item, typically 9+, as those will be the cheapest, then buy a few of them and sell them somewhere they are worth more than the listed price.

Black powder that is, not white!

Most towns sell powder, the stock varies from town to town. Azaq-kale in the SE corner is a special case as it typically has large quantities of powder (and spice) for cheap.

Unlike the other trade goods you should buy any powder you see in towns. You will very rarely see it in villages. You then sell the powder to castles. Be aware that not all castles appear to be castles, some of them look like towns but are actually castles. I'll list the towns here, I suggest you write them down:

Sweden:
Koenigsberg
Reval
Riga

Cossacks:
Chernigov
Kiev
Sich

Poland:
Krakov
Lviv
Smolensk
Vilna
Warsaw

Muscovy:
Cherkassk
Moscow
Pskov

Crimea:
Akkerman
Azaq-kale (much powder!)
Bakhchisaray
Kyzkerman

You can sell them in any castle. Powder can be bought for 100-250 and at 0 trade the price range are usually around 600, 800 or 1000! I would suggest not selling powder for less than 800 unless your inventory is starting to get full as supply is considerably lower than demand. You tend to get 3-4x your investment for every powder you sell, this will remain a core part of your financial gains and I would suggest just keeping things simple and only trading in powder. 80% of my early game profits came from powder and I feel like I needn't have bothered with anything else.

All fiefs give taxes but cities give the best of all. I typically get in the region of 20,000 taxes a week from a single town that has most of it's buildings and staff purchased. They do however require substantial investment to get started but considering the low price of troops wages it's recommended to get started early.

Gather 50-100k money from selling powder. Go to the polish mercenary camp and buy a single mercenary horseman, than choose to change his equipment and buy top of the range armour, a kelkan shield and saber (kelkan is much lighter and faster than steel), a fast horse and some kind of musket (not a carbine, you don't want them trying to shoot from horseback)

Now buy as many of these uber horsemen as you can and join a faction that isn't Crimea, if you can't join properly then join as a merc. Now go hunting lords with your monster cavalry force, just start the fight, line them up and charge. If the enemy makes a wagon circle then use the map and click behind the camp to move your force there before charging, there's, a gap behind the wagon wall they can get through!

Doing this you will get lots of renown which increases your army size and chances of being recruited. Join a faction, preferably Cossacks, then go siege one of the Crimean cities, preferably Azaq-Kale. Crimeans use bows with their muskets, and bows suck without high power draw, so your heavily armoured dismounted cavalry will easily cleave through them.

Your leader will probably give the city to you, if not then pick another or take the city back after Crimea sieges it again. Once the city is yours dump all your cavalry in the roster and go buy a ton of mercs from the cossack camp, doesnt matter the type, and dont bother upgrading them you only need numbers to deter a siege and you want to keep them cheap

When your garrison is at about 400 you can stop, the garrison will automatically generate more soldiers.

Continue doing your powder runs and use the money to develop the city. Just talk to the mayor and pick buildings and appointing people and try to get everything and everyone built and hired. Your city will be poor because you sieged it but over time it will build in wealth and prosperity, and Azaq'Kale in particular is a very wealthy town. Be sure to deposit your cash in the merchant guild once you have built it for super interest. You can also buy custom equipment for cheap in a city you own!

And if you are feeling especially greedy you could go and grab up another town! Just be aware it gets tedious clicking through all the staff wages screens every week D:

Once a Merchant Guild has been built you can store your money there for safe keeping and interest. I've heard that if a city is taken by a rival faction they take all your money from the bank but I cannot confirm this. I have never seen Azaq-Kale sieged by anyone but me, even after 1000 days, and if you yourself control it you can ensure the protection of your money.

Interest is 14% per week. If you have 100,000 stored then it's 14k per week. If you have 1million stored then it's 140k per week! Custom mercenaries and gear orders are VERY expensive but if you can work your way up to 1mil then you will never need to worry about money again, the interest will pay for everything!

There is one thing I need to say about this though. The actual process of adding money is very misleading. When you click to add money to the bank it puts all of the money you are holding into the bank. So if you then click -2000 you aren't putting 2000 into the bank, you're taking 2000 out! At first I was trying to put everything in except 5000 for powder trading and started thinking there was a maximum of 5000 per bank when in fact I was putting all my money in and then taking all but 5k out! Don't get confused like I did, just click to add money then click -2000 a few times.

So, in a nutshell:
1) Get money through letter delivery, tax collecting or caravan escorting. 1k will do.
2) Buy powder from the listed towns. Sell to any castle for 800+ (you should buy some cheap horses with your early profits to keep in your inventory and keep the weight of the powder from slowing you down)
3) Optionally trade in other things as well
4) Save up 100k then get a well geared polish merc cav army, farm renown, join a faction and capture Azaq-Kale
5) Garrison Azaq-Kale, develop city while powder trading
6) Collect taxes from Azaq-Kale, continue powder trading, deposit most of your money in merchant guild in your town to generate interest
7) Optional: Capture more towns for more tax revenue (warning, it gets really annoying to click through all the staff wage windows at the end of the week!)
8) Get to point where interest excedes expenditures, you now have effectively infinite money!

I hope this guide was helpful. I couldn't find help at first, all the guides were dated, and bandits hunting was grindy, frustrating and unprofitable. The methods I have described will help you bypass this and get into the heart of the game: Conquering Eastern Europe With Fire and Sword (and a majority share in everything)!