Like most of us, you probably have particle board under the carpet. As a result, I would suggest a "dry" carpet cleaning machine, which uses a sawdust material. They are available for rent here at supermarkets. The other option would be to use just a little water and quickly vacuum it up, using the least amount of shampoo or soap you possibly can.
I've used Simple Green, but only a tiny amount, to get stains to dissolve in the water to be vacuumed up. I've then had to re-moist and re-vacuum over and over again to get all the soap up. So, if you decide on this method, to save you a lot of work, try just using warm/hot water sprayed on the carpet, a small section at a time, and then vacuum it up. I do sections of about a foot or two foot square each time.
Just be careful not to use a lot of water. And, the less soap the better. Much less soap. No matter how much soap you use, it will be too much. Soap residue attracts dirt like a magnet.