How do I find Pokémon?

If you look around on the map you will be able to see all the different icons such as Pokémon Stop and Pokémon Gyms. If you look closely you will be able to see a "leaf-effect", this indicates that there are Pokémon in that area.

Go there and you will encounter Pokémon.

In addition to the other answer, if you see a loading icon (rotating circle) at the top left corner for a long time I recommend killing the app and launching it again.

I had the same issue where nothing would show up, turns out the game lost connection and couldn't sync with the servers.