Vassal of My Vassal is My Vassal
Vassal states are the other big feature of Warlords. In fact, it's probably the main addition in this expansion. Vassal states enable you to subjugate beaten civilizations to your rule, or become the protector of other civs during peacetime.
The basics are as follows. Once you discover Feudalism, vassal states get enabled. There are two types of vassal state agreements – peaceful and capitulation. Capitulation, as the name implies, is possible when you've beaten someone in a war big time. Peaceful agreements will usually happen between good friends. Both of them result in creation of a vassal state.
Vassal states have no diplomatic independency. Their peace/war status will always reflect that of their master. If the master declares war or is declared against, the vassal is obliged to also declare. On the other hand, if someone declares war on the vassal, then the master also declares war automatically. The master experiences a slight happiness bonus, and the vassal a slight hit in this regard. Also, the master can demand tribute in the form of any of vassal's resources – these demands will usually be granted. If not, however, it automatically means war. Also, masters can demand gold or technologies from their vassals, and the chances of these demands being successful are also higher than outside a vassal relationship.
Vassals won't just automatically love their masters though. If you make someone capitulate, they will probably still hate you. You can build up your relationship and get better relations, but this mechanic is, in all honesty, rather useless. I failed to notice a significant increase in the vassal's willingness to cave in to your demands if they're Pleased. My vassals usually stay Annoyed, and give me what I ask for most of the time.
If you want to, you can gift the vassal your technologies. Then he might research techs that you don't research and give them to you, but there's also the danger of your vassal selling these techs to your enemies. They do not seem to particularly care if the civ they trade with happens to be your enemy.
To make someone capitulate, you have to be in a real position to exterminate them completely. Civs won't surrender if you just have the upper hand in a war, although they're now smarter about giving you techs in return for peace. They will not refuse point-blank to do that peace, as they often would in vanilla. Once you are really in a clear position to eliminate the civ completely, maybe with them down to two cities, they'll be willing to capitulate if you ask them to, or even offer to do so themselves.
Whether you accept capitulation is up to you. It has two significant downsides. First, you'll pay increased maintenance, as your maintenance costs increase with the number of vassal cities. If you are finishing a war that has nearly wrecked your economy, accepting surrender may just kill that economy off, and that's not a good idea. Second, as the master, you have no way of breaking vassalage. A capitulated vassal may not break it either. The culture from vassal's remaining cities will still remain, and, if you took some cities from him, it's likely that they will fall under the cultural influence of one of the remaining cities – which you can never dispose of. Or the vassal might decide to occupy some “holes” that have formed by building new cities, denying you any chance to do anything about it, and increasing your maintenance costs at that.