How do I send an envoy?
Solution 1:
You are currently looking at the City-State Details screen -- which is to say, at a specific city state. You need to look at the City-States Overview tab instead, found by pressing the button circled in this picture:
From this tab, available Envoys will be placeable by pressing the + / - buttons next to their name under the "Envoys" heading. (Actual buttons are not drawn in MS Paint)