subject asks it all

Carpet shampoo, a soft brush, and a good vacuum.
Unless you have all-weather floor mats, then just blast them at a self car wash.

mine are all weather mats. I just hose them down when I wash my car. I do need to get some new ones though, they're getting pretty beat up and have a chalky appearance now

Soapy water or any type of detergent works fine, but it makes them more prone to attracting dirt again (as with any carpet shampoo).

When we detail our customers cars, we use an enzymatic cleaner to actually dissolve the stains, and then a product called Capture (it's for carpets, I think Home Depot sells it) to seal it and make it smell fresh.

get some automotive carpet shampoo, a bucket,a piece of plywood, a soft brush, a medium stiffness brush, and some clips. hang up your mats, fill up the bucket with shampoo and wateruse the soft brush for application, then use the other brush to get up the dirt, then blast it with water until no more dirt comes out or as little as possiable, vacume it up, hang it up and let it dry. then spray them with some deodorizer. thats how i did it when i detailed and it works really good