This is a very short guide on how to develop your kingdom in one of many possible ways.
The example presented on screenshots is the kingdom of Morocco, on easy difficulty, in a late time period, around 1350 A.D.
You start with a marshal and practically nothing except a few structures. If you are lucky, you have an income of a couple of coins. If not, then you need to work hard to get more coins flowing.
BTW, if you have chosen for example a Catholic kingdom, you have an additional income (taxes) coming from religion. Though the pope can call crusades against any kingdoms and choose your marshal to leave your kingdom for a crusade, which is little profitable.
Anyway, you have to obtain some additional gold coins from somewhere. You can start building Tax Collector's Offices, Markets and Docks (and then Harbours), or increase your Kingdom Power.
The nicest way, IMHO, is to appoint your royalty, the king and princes, merchants. First offer trade agreements to strongest (largest or otherwise) kingdoms. Then recruit your king and princes as merchants, choose trade with kingdom option, select the kingdom that gives the largest income, and finally trade for gold.
That's it, the first step that is actually an economic growth. Also keep note of your relations towards other kingdom, you need to keep them sufficiently peaceful or begin to build more military structures and arm your armies properly. Avoid to make any non-aggression pacts and alliance agreements unless they are with large kingdoms or with kingdoms that you will avoid to attack in closer and further future (you'll have to break agreements to attack closer neighbours that you have agreements with and thus lose kingdom power).
You can promote more regular merchants (each one costs 1000 coins) to trade with other kingdoms for gold. You can use all 8 slots. To have a free place back, you need to make your (regular) merchant either govern a province (to have him do something different if you wish to keep him after all) or exile him. Yes, instead of stopping trade which causes you to lose relations with a specific kingdom.
At this stage of play, Kingdom Power becomes more and more important. Whenever possible, you should be raising its level steadily. You also need buildings such as Tax Collector's Office to generate more gold coins, but you can avoid structures such as mosques and churches now. If you are at war with a kingdom by chance (and it won't accept peace), then you need also erect buildings such as Granary and Bakery to have increased food production and increased food storage for recruiting heavier armies.
If you avoid to lead your armies in battles and play only in the main game view, you can recruit mostly cavalry to your armies because it's fast and strong.
To conquer provinces, first recruit your marshals, appropriate (strong) armies (may be composed of cavalry), guide your marshals to towns of a specific kingdom, most conveniently your two armies surrounding one town, when finally your marshals surround at least two towns of a specifc kingdom break agreements and declare a war on it and then start a siege on each one of them. Should be easy if your economic growth progressed smoothly.
When you have conquered some provinces, you'll begin to be in a dire need of more mosques and churches. Why? Conquered provinces have something known as Nostalgia, which means that loyalists and rebels will always haunt your newly taken provinces as long as you won't adopt population of conquered towns with a Cleric. To adopt population, you need lots of books (about 600-1000 depending on the time passed since a takeover) and just one cleric.
You can expand your kingdom, recruit more marshals (in place of merchants) and request vassalship from any kingdoms that you don't need to bully anymore. Always keep one cleric though. And yes, when you have more provinces and marshals, you can make up for a gold coin loss (increasing costs of marshals) with vassalships.
So, to sum everything up:
1) offer trade agreements to largest kingdoms
2) appoint your royalty (the king and princes) merchants and trade with kingdoms for gold, recruit more merchants to generate more gold coins
3) keep relations with other kingdoms peaceful, though avoid any alliances and pacts of non-aggression
4) grow economically, then you can recruit about 3 marshals and attack nearest kingdom (breaking agreements if you have any)
5) keep the pace up erecting additional buildings, including mosques and churches, and then promote a cleric to adopt population in towns you have conquered (if you've chosen a war campaign instead of a peaceful development)
And that's actually all. From this point on, you can learn on your own how to manage your kingdom. Perhaps worth noting is that you need to avoid to have your kingdom at war with more than 2 kingdoms unless your kingdom is a very powerful one.