First of all, there is inheritance. You want your heir to be of your dynasty, because otherwise you loose the game. The blood drop in the upper right of the portraits is whether they are of your blood line. Next there are the succession laws. They determine inheritance. You want to get to primogeniture, which is very hard if your a vassal. In primogeniture, all your titles go to your first born son or daughter, depending on your gender laws. Gavelkind is the worst, since it splits up your titles. That means less territory you control directly, so less income, and less levies. You want to keep your children in your court until they are married, so they marry. The AI sometimes either waits too long to marry or does dumb stuff. You want to invite claimants to titles to your court because you can press them. This is helpful, because they are normally inherited at least one generation, and marrying them into your family can get your family more claims. But you have to watch out for your family, they want your titles. Levies you can raise of vassals are based on the laws, and their opinion of you. You also can raise levies from your own personal demense, the land you own yourself. Marry young people so you have more kids. You want enough heirs so that if something happens to one of them, there is still someone of your bloodline/dynasty to inherit. Too many siblings can be problematic however, as they all will have claims when your child inherits. To declare war on other Christians you need a claim. You can get one through marriage, or passed down from your parents, or inviting a claimant to court, or fabricating one with your chancellor. Make sure your vassals are happy. Watch out for succession, as you will get a short rein penalty for 9 years. This will make vassals dislike you more. One plot they can do is to institute elective monarchy. This makes it so any noble can become heir, but all vassals vote. So, if your vassals like you enough, you can pretty much choose heir. But it is dangerous if they don't like you. Assassination is a helpful tool, but dangerous. People can hate you and maybe revolt if you are caught. Make sure you marry your children off. Your wife may plot to kill you. Be wary of any and all family members, but you can trust them more than a normal person.
Just some basic advice. Very jumbled up, but hopefully you get something from it.