Taking Over City States?

This may be a dumb question, I'm another new comer on here. Bought the game last night and can't stop playing it.

I started a game on a huge world map with the max AI players and max city states. I'm surrounded by 3 city states, two of which I'm friends with.

The one closest to me, is also the friendliest to me, has a lot of resources, and just land in general I'd like to have. How do I "take over" the city state?

Is it worth going to war with them? They have no allies, and I'm the only one offering them protection. Or should can I achieve having them as "mine" just by becoming allies?

I find it difficult to hold on to the allies status after getting it....so just wondering, should I go to war with them? What do I get out of it?