Why Is Money Important?
If military might is the power tool with which you carve out your kingdom, then money is the fuel with which that tool is driven. If you cannot pay your soldiers, they will, aside from any other penalties, not be as effective in combat, as their morale will be lower. As such, if you are facing an opponent of near equal strength, you will lose.
Beyond that, money is also what allows you to recognise your military potential. You can have all the technological advancement and vast expanses of land you want, but it's worth exactly nothing if you can't develop it beyond its basic structures. Having a strong economy means that you can be fielding vast and varied armies, supported by mercenaries if necessary, that will be capable of taking on the forces of much larger nations and winning through concentration of might. If you have a small but advanced realm, and you are fighting someone who is spread across a vast distance, you will be able to raise and concentrate armies quicker. You will also be able to afford stronger holdings, and more holdings, making you more resilient on the defence as well.
Finally, as in real life, those who have money have more opportunities to make more. Get a powerful economy working early in your demesne and more expensive economic structures become available for purchase without a prohibitive wait.
Beyond that, you need money for other purposes. A rich king can assassinate his foes and placate vassals where a poor king cannot.
So, you know why it is important to have money. Now, how to get rich...
Prioritize, then Build
Kings who wants an army and money to pay for it know that the money comes first. When you start the game, hold off building those military structures or their upgrades for the moment. This means forfeiting an early military advantage, but for the purposes of this guide, I'm assuming there's nothing immediately within reach that you must seize.
Take a look at your holdings, and the income from each. Look at the taxes. Cities seem to bring in the most, yes? True, but wait a second and consider; who owns your cities? Not you, but your vassals, and vassals don't always pay their taxes. Churches are even more reluctant, and other baronies net you nothing at all. So upgrade your primary holdings first; get the castle village built up to a castle city before you build anything else.
Once you've done that, you can start upgrading your other buildings. Go for the cities first, get the ports and the taxation buildings upgraded as far as you can. This will give you a considerable second source of income that will rival your direct holdings at times where your mayors like you and are willing to shell out. It's unreliable, but it's there. Once you've done that, move on to your churches.
You may want to consider upgrading your baronies as well. While not directly providing money to you unless you raise taxes on your vassals, which angers your counts and dukes, it will allow them to develop their own lands, providing you with extra soldiers and increasing the rate of development of your kingdom.
The reason it is important to get all your economic building done early is because the longer you have these structures, the more money you will get by end game. If a structure gives me 15 gold per year, and I build it in 1200 instead of 1250, that's an extra 750 gold by end game.
There still needs to be an element of common sense applied however. If there are only a few decades left in the game, I might benefit more from that last barracks upgrade to squeeze out some more soldiers for that final push for prestige. I might not even make the money back on that expensive final upgrade to my economy. But generally, you want to go for economic upgrades.
Befriend Your Vassals, And Only Then Jack Up Your Taxation
Taxation works via two mechanics; laws and opinion. Raising taxes on your vassals will increase your potential income, but vassals will only forward you the money if they actually like you enough to do so. Therefore, you need to ensure that your vassals opinions towards you are at least positive before you move towards higher taxation. Otherwise, although your taxes on paper should be higher, your actual income may actually be reduced, because the higher taxation irritates them. In addition, you'll lose soldiers. Once your vassals (or at least a majority of your vassals) like you enough, start raising taxes. Raise city taxes first (ensuring your mayors like you of course) as these give you the most income, then get your churches paying you money. Strangely this doesn't anger the pope. After this, you can consider taxing your major vassals and barons. However, while this nets you more money, it weakens them and reduces their opinion of you, and unlike your minor vassals, your realm vassals can do you serious harm, and are also likely where the majority of your soldiers come from if you are a major kingdom.
Taxing your minor vassals also makes it a lot more worthwhile upgrading your cities and churches, and allows you to realize the full potential income of your held counties. It's particularly valuable if you don't have a whole lot of counties to work with in the first place, as the greater concentration of wealth allows accelerated development.
Decreasing the levies demanded of cities and bishoprics can go a long way to counteracting the negative effects of higher taxes. Even when set to their minimum levels, you'll still get some troops from your mayors and bishops...and decent amounts of them if they like you. The extra money you get can be used to more aggressively build troop structures in your holdings to make up for the smaller levies from your mayor/bishop vassals.
Unleash Your Inner Viking
War is, as in real life, a very good way of making yourself a neat little fortune if you plan it right. By looting a series of holdings, partly cities, an then sprinting can steal a sizeable chunk of money at the cost of a rival kingdom.
This, however, requires some planning. The first thing you need to check is whether your army is strong enough. You can also click on the little graphs chart on the bottom of the screen and get a review of the enemies resources army size, etc. If you've recently bled your army white, you obviously need to let it recover before you go launching any raids.
Secondly, you need to consider, when looking to attack, who you are attacking and also what your excuse is. If you're joining a defence against a holy war, great. Your enemy will likely be tied down fighting on foreign soil, if his army hasn't already been destroyed. This means your army can focus on storming cities and churches, mosques or temples, without having to worry about enemy armies ruining your chevauchee. If, on the other hand, you're launching a holy war of your own, you're likely to attract the ire of other characters of that faith. This can escalate things up from battling against a small, seemingly isolated target to waging war against half of a particular religious world. Also, it means you're left with territory you may not want, which can be taken from you at great expense later as all that money you sacked is taken back. As such, the best raids are launched defensively against an opponent that is already embroiled.
Sticking with this second point, it is also important to examine where you are raiding. Remember that even the richest cities are unlikely to yield more than 20 gold after being taken. Some will yield less than 10. A few may yield riches later on, but this is likely to start happening when castles develop and raiding becomes more expensive. Raiding is in its heyday in the early game where castles remain underdeveloped and strong armies can knock them down one after another. There are three considerations to take into account before setting off.
1) How much will this cost me personally, and how much will it cost my kingdom overall? You may be able to pay for the war handily, and the monthly cost to yourself may well be outweighed by the loot you get, but consider the expense to your vassals. If you have a personal army of 2,000, and your total army is 12,000, then if that 2,000 man army costs you 4 gold per month, then your total army probably costs the kingdom 20 gold a month. That means that you need to have stolen more than 20 gold per month, over the course of the war, to have made things worthwhile for the kingdom. If all you want is personal enrichment (see Keeping Your Vassals Weak for why weaker vassals may not bother you) then this is fine, but be aware it may reduce your power in the long term. If, on the other hand, your goal is to build a mighty kingdom overall, then bleeding your vassals dry is counter-productive; they will not be able to build as much and the benefit to your demesne/ability to gift money will not counter the deleterious effect upon your vassals. Taking into account reduced costs from attrition, your expenses may fall, but plan ahead. If you've brought a navy into things, which you probably will have to for speed of deployment, that raises your costs even more. Be sure to send navies home when you don't need them, but have them ready to bring your men home again quickly so your soldiers aren't dawdling in enemy territory spending all your loot on women and wine.
2) How strong are the defences, and what is behind them? You generally want to be attacking with at least 15 times the force of the defenders in sieges. You definitely want at least 10 times. Any less than a ten to one advantage and your army will be mauled. Of course if you only have a few cities to take you may be able to get away with less, but if you're trying to sack multiple provinces then you need this kind of advantage and you need to maintain it. If I set off with a 20,000 man army which costs me 40 gold per month, and it takes me 2 months to get to the combat zone, yet I take 12 holdings at an average of 15 gold per holding, and bring the war to an end and get my men home in 5 months, the last 2 of which are spent at half maintenance due to casualties/ships being sent home, I've made a net profit of 20 gold. If in the same operation I get mauled badly and only take six holdings, and return a month sooner, due to misjudging the strength of the defenders, then I've lost 30 gold. If we add another month and take 16 holdings, I take home 100 gold.
Hopefully profits will be better than that, but that demonstrates the principle. How much will it cost me to get there, how much will I get when I arrive, how long will I be in the field, and how long will it take me to get home. That's the maths you need to do.
3) Where are the enemy armies? If you're going to get bloodied the moment you arrive, then you may want to stay at home, unless you're lucky enough to capture someone important (see Ransom, Ransom, Ransom! for more details).
On a final note, remember that retaking an allied castle yields you no loot. Unfortunately the enemy has already taken everything there is to steal! On the other hand, if an enemy retakes their own holding, you're free to siege and plunder again.
Ransom, Ransom, Ransom!
Another perk of warfare is the money you can get from ransoming major figures, and you can also get this from arresting nobles within your lands, although this has a deleterious effect upon your vassals. Courtiers net you 10 gold, minor vassals get you 25, counts net you 70, dukes 145 and kings net you a whopping 225 gold! Always check your dungeons for people you can ransom. It's an irregular source of income, but you can make a fortune off of it, particularly if you're lucky enough to capture a major figure. This is the one time where it might be worth going after enemy armies; one count could pay for your war! It's a gamble, but take it into account during your raids and warfare in general. And it can cut your vassals down to size too, if you're having problems with them.
Tithes and Offerings
Don't neglect Catholicism as a huge moneymaker. In catholic kingdoms, religious vassals (e.g. bishops) will not pay taxes to you unless they like you more than the Pope. If you're willing to risk excommunication free investiture can bring in a very nice revenue stream, and will improve relations with your noble vassals as well (which will, in turn, increase the amount of tax they're willing to pay). If you're really well established consider replacing the Pope with one of your vassals and watch as the collective wealth of Europe pours into your coffers each month!
Odds and Ends
Get married! If you get married your king can recieve a sizeable payment in wedding dues, or a sizeable prestige boost if he declines. Often this can be enough to pay for construction... or to bump off someone you don't like. Even if you don't want kids, marry some elderly spinster or celibate figure if you've got all the heirs you need and get that money.