Why don't satellites run out of fuel?

Can you explain to me why satellites do not run out of fuel in their orbit around Earth? I understand that satellites need to be propelled into space and stabilized in their orbit, but once they're there, how do they maintain their position without needing a constant supply of fuel? Is there some kind of mechanism or force that keeps them in place, or do they have a way of conserving fuel that we're not aware of? It's a fascinating concept and I'd love to understand it better.