I've used a steam cleaner before on cars other than my Lexus, and, as it turns out, have been very lucky that the whole liner didn't sag and go to hell. This was before I knew any better. Maybe the pros can do it and get away with it, but for us amateurs...
I recently did mine with a Woolite product called Oxy Deep that is actually made for carpets (there are other "oxy" products available - I just knew and trusted Woolite). I sprayed it on, let it sit for a few minutes, gently wiped it with a damp sponge, and vacuumed it when it was dry. Came out clean and smelling fresh, with no damage.