Thank you! The gun is found in the top right corner of the map, it should be visible on your character after you pick it up. You can shoot with button 1 of the gamepad (Xbox A/Nintendo B/bottom face button), Ctrl, or Shift, and aim with Left Stick/Arrows.
If you're trying to play the browser build with a gamepad, it is possible that your model may not be fully supported - I sadly discovered too late that the gamepad support in the browser isn't quite as good as with Windows, in which case I apologize. However, trying the Windows .exe version might help! (And if it doesn't, then it must be some kind of bug that I never discovered, in which case I also apologize!)