How can I access my Pokéballs in Pokemon Go?

Pokeballs can only be used when you encounter a wild Pokemon. The Pokeball will appear at the bottom of the screen and you can swipe it up to throw the Pokeballs at the Pokemon in order to catch it.

If you are in an encounter you can tap on the bag icon to swap balls, for instance Great Balls.

It sounds like you are not in a Pokemon encounter, in that case the only thing you can do with Pokeballs is to discard them by tapping the trash can icon to the right of the Pokeball.

To encounter Pokemon while you are walking around, they will randomly appear and you can then tap on them to begin the encounter.