I have a pressure washer at home, and that's what I've used on my carpet. To really answer your question though, yes, just water through their pressure washer is what you want.
When I've done mine in the past, I'll get it a little wet first, and spray some carpet cleaner on it, and get down on my hands and knees with a scrub brush and really work the carpet well. Once I've scrubbed, I'll use the pressure washer to push all the dirt and soap into the bilge. This may take a while. Soap will keep coming out of the carpet. Try to get it all out, or the carpet will get dirty easily again. Once everything is washed out, I'll use a wet-dry vac to suck as much water out of the carpet as I can, and then let the rest air-dry.
If you're going to do this at a car wash, bring plenty of quarters! It will take a while to get all the soap out of the carpet. You might be better off borrowing a pressure washer if you don't have one.