There are actually two ways:
One is, as he said, get his land/population into the threshold where he has the option to break free, and then tick him off until he does so. You can mouse over his name to see where he's at, but basically:
- 50% land area of his master, or
- 50% population of his master, or
- 50% land area since when he capitulated (i.e. you're doing a really crappy job protecting him)
The other method is to demand resources as tribute. As opposed to demanding techs, cities, or civic changes, resources he
has to give free of charge, or else its automatic war. So see if he has a lot of resources and demand them all from him. (you don't even get diplomatic penalties) If he isn't completely scared of you, he may refuse. Even if he doesn't, you still get a lot of free resources.