Great you got a vassal under your control by voluntarily or by force(liberation or capitulation same thing really).
Now what?

Treat them well. As long as you have never initiated a taxation policy or maintained a heavy one for a long period of time, they will most likely never revolt as they will probably just enjoy your protection for free and you will enjoy their bonus yields for free because you aren't taking their yields.
Failing to protect their lands have never been an issue in cases of rebellion as if they're getting smashed in their own lands, they don't even have a chance at rebelling at which you can quell them easily.
Vassals will often revolt when you are busy with other wars. Perfect timing too. Take precautions of that.
Relax your taxation policy and trade with them often. The +20% Tourism is there, so you can easily gain influential treatment.
Give them free open borders. This may or may not be a bad thing but it improves your relations and management significantly.
Let them have a city if they so want it so bad, but make sure they pay well! I've often noticed as a master of Venetian puppetry that the AI will often want one of their most important city which is usually a port or city that is so important to them that they want it back via trade or force. It might not even be the capital!
And most importantly check out http://civ-5-cbp.wikia.com/wiki/Vassalage for more information. Have fun folks!
Now what?

Treat them well. As long as you have never initiated a taxation policy or maintained a heavy one for a long period of time, they will most likely never revolt as they will probably just enjoy your protection for free and you will enjoy their bonus yields for free because you aren't taking their yields.
Failing to protect their lands have never been an issue in cases of rebellion as if they're getting smashed in their own lands, they don't even have a chance at rebelling at which you can quell them easily.
Vassals will often revolt when you are busy with other wars. Perfect timing too. Take precautions of that.
Relax your taxation policy and trade with them often. The +20% Tourism is there, so you can easily gain influential treatment.
Give them free open borders. This may or may not be a bad thing but it improves your relations and management significantly.
Let them have a city if they so want it so bad, but make sure they pay well! I've often noticed as a master of Venetian puppetry that the AI will often want one of their most important city which is usually a port or city that is so important to them that they want it back via trade or force. It might not even be the capital!
And most importantly check out http://civ-5-cbp.wikia.com/wiki/Vassalage for more information. Have fun folks!