To complete a stage you have to clear all the fire in every room. Once all fire is cleared, you should return to the entrance and leave. There is a faint green glow at the edge of the screen in the direction of the entrance. You can follow this if you have lost where you came in.
Use a combination of Hose and Extinguisher to clear the fire. Wet all surrounding areas with water as this slows fire spread. The extinguisher will put fire out quicker, but doesn't stop spread again and you have to get closer to make it efficient.
When firing the water, put it from side to side in a snake. This gives better coverage than just firing straight ahead.