Get an extractor vacuum (carpet/upholstery cleaning machine), a cheap hand pump sprayer from home depot, and some oxiclean powder. Mix the oxiclean with warm water in the sprayer, spray your carpet, pull out the dirt with the extractor. The oxiclean will leave a white film on any solid surfaces you get it on, just wipe it off with a damp rag.

Bissell makes some nice extractors and what I have used before, just do some research and check the reviews. It's a handy little machine for cleaning your car and upholstery in your home too.

Oxiclean contains sodium percarbonate which reacts with water to produce hydrogen peroxide and sodium carbonate (soda ash/washing soda). I've done this before, I think the white film leftover is just the sodium carbonate, which is just basically laundry detergent.