I do detailing as a side job and have seen the worst of the worst and cleaned it in a similar way as skyZ. I take the front two seats out, lightly wet the carpet with a good spray bottle and spray simple green heavily on the carpet. I do a light scrub and let it sit for about 15-30 minutes. I then come back and spray simple green again and scrub the heck out of it. When I get all the worst spots out, I use my super wet dry vac and suck everything out. Spray with clean water, kinda heavy and vacuum again. That's for carpets.
Seats are a little different because everything soaks in. Try spray on stain remover for clothes in the shade, wet lightly with water and wait a few minutes.
Scrub then vacuum. Spray lightly with water again to flush and vacuum. Let everything dry in the sun for a minimum of eight hours or 24 hours in a garage. Make sure that the carpet is bearly wet before putting up to dry or vacuum again.
I have a job this weekend that is the second worst job I have ever done and I have all the right chemicals and equipment. I usually charge between $100 and $150 to detail a pitted car. They always turn out nice. No complaints so far!
If a stain won't come out. Some time in worst case scenario, use purple power or brake cleaner and IMMEDIATLY scrub and vacuum. But that is worst case scenario for grease stains. Sometimes the carpet is just warn and needs to be replaced. But so far I have never had to replace carpet.
Chris