PewPewIO throws you into a small arena with other players. From there on out, it's a dog eat dog kind of world, with power-ups to allow for one dog to briefly become super dog.
Simply use WASD to move, the mouse to aim, and the left mouse button to shoot. Right click to "push" which boosts your ship forward and lightning speeds. You'll bounce off walls, ping ponging across the map. Any enemy you ram while pushing will take damage.
Learn the power-up spawns. That'll allow you to more easily grab them for yourself, or to intercept other players who are trying to capitalize on them.