How to get Pokéballs in Pokémon Go?

Next to PokéStops you will only receive Poké Balls, when you Level Up or when you use the Shop.

The Poké Ball's successors (Great Ball, Ultra Ball, ...) are currently not purchasable in the Shop yet. They can only be received with the two former cases.

As far as I know, most or all PokeStops and Gyms in Pokemon Go are taken from the game Ingress, which had few set Portals from Niantic and most Portals requested by Players. Which leaves a possibility that no one ever set or requested Portals at your location.

If you and your friends are certain, that there are no connectivity or GPS issues I second dly's comment:

Until recently you were able to request Pokéstops, but apparently they took it down again. If you have no stops in your area at all it might still be a good idea to submit a ticket at support.pokemongo.nianticlabs.com/hc/en-us – dly 3 mins ago

You can either retrieve them from PokeStops, get them while leveling up, or purchase them from the Pokemon Go store.