I do a little carpet restoration, when it's not rotten (the substrate rots, the actual fibres don't...) One rule of fibre; it you clip a small sample, and burn it with a match or lighter, and it melts, its not organic (i.e., wool) If it's wool, when burned, it will smell like burning hair and burn, not melt. Assume that ours is Nylon after the test.
On the sets/pieces that I have done, this is my process...Take care when removing carpet or some of the glue will release and other places where it doesn't, it'll rip fibre from the backing and now you have to repair or throw it away, wasting great volumes of profanity...Repair is another tale, for another time...
Lay the pieces out on cleaned concrete, and vacuum the back/bottom side first; this vibrates the dirt, sand, etc loose towards the concrete. Amazing what falls out. Remove pieces and vacuum concrete. Flip and vacuum the nap side. Repeat above steps. Now you can proceed to washing. I use a combo of Dawn dishwashing liquid in hot water (good at cutting grease), and add about a tablespoon of citrus cleaner (I like Citrasolv valencia orange, Murry Fowler's favorite..). Now the part that sucks, the elbow grease. I use a large tire brush, the kind with a short handle, and on hands and knees, brush/scrub the carpet at least two directions, usually four, and then do the back sides. Then rinse until water runs clear. Then I hang up to dry, as Peter said.
When done, if there are persistant stains, the best stuff I've found is Nature's Miracle, found at pet supply stores. Wonderful product, that is probably an Oxy-type product, I don't know...only know that it works on organic stains (not paint or axle grease) with no harm or bleach.
Then I spray front and back thoroughly with extra strength Fabreze for fabric, and allow to dry. It dries quickly, and the smell is fresh but not goofy. Don't use the scented variety.
I had a set that I had my carpet (household, probably an oxy product..) cleaning guy do a set, and they turned out good, but I then washed one piece as above, and there was still obvious dirt, so I guess it depends on how clean you want it, and if you can physically can get down on all fours and scrub. This usually requires two beers, depending on ambient temp.
In the category of "while you are at it...", I usually clean off old glue (another job that sucks) from the backside, take blue painter's tape and carefully mask the vinyl trim, where present, and spray the back side with black Flex-Seal, the stuff you see on the telly for gutter leaks, etc. Two cans should do a full set of carpet. Lay down paper...warm dry day with no wind, and spray out side. It stinks. Allow to dry until not tacky, remove painter's tape (carefully) and allow to cure a couple of days, in a dry garage, etc. Again, it stinks. "She" will not be happy if you bring it into the house. If you are doing any of the four floor pieces that have the chrome clips, remove them (before you spray the Flex-Seal) and buy new ones via the internet; they are cheap. Install after backing has cured. If you have to stack/box up for a while, put wax paper between pieces, as sometimes an unknown tacky area will screw up your nap on the piece under it. Learned this the hard way...Its not a perfect product, but the best I've found to bond to the back side, and add a little sound deadening at the same time.
None of the above is recommended in the winter.
Also, the driver's side floor piece will always be more worn, and the nap will often not return. It's fifty years old, and physics is physics.
Hope this helps, sorry so long winded.
