I'd use some Griot's Interior Cleaner first. That stuff has been a life saver for me (I just ordered a gallon of it, after running out of a 35oz. bottle). It has taken out coffee stains, grease stains, and other stains of unknown origin from carpets, seats, trim and headliners.
If you don't feel like ordering any of the Griot's cleaner, try some Prestone foaming cleaner. I've used this with good results as well. Finally, you could try a regular carpet cleaner, like you'd use on your home floors, but test for color fastness before trying that.
HTH. Good luck with the dirt!