In order to communicate with a city-state, you must find it first. When one of your units encounters a city-state, the city-state will tell you what type it is, and if you're the first to discover it, you will automatically earn an Envoy with that city-state. Once you have met, you will be able to undertake "quests" from that city-state. If you want to get in touch with the city-state, you can click on the city itself, or you can go through the City-State Panel.
Communicating with City-States
In order to communicate with a city-state, you must find it first. When one of your units encounters a city-state, the city-state will tell you what type it is, and if you're the first to discover it, you will automatically earn an Envoy with that city-state. Once you have met, you will be able to undertake "quests" from that city-state. If you want to get in touch with the city-state, you can click on the city itself, or you can go through the City-State Panel.