This is an interesting threat to me because I sell carpet cleaning equipment. Most if it couldn't be used on a boat because the machines are too large.
Basically carpet cleaning can be broken down into four steps.
1. Remove debris usually (pick up the big chunks and vacuum).
2. Apply chemical / water solution. Usually the carpet will be cleaned more effectively if the chemical solution is applied and allowed to dwell before the water is applied to the carpet. If you are using a machine then put only clean water or a rinse agent into the machine, this has the effect of rinsing the soils and chemicals out of the water.
3. Agitate. This can be done by the bushes on a carpet cleaning machine, a manual brush or with water pressure. Agitation helps to bread the soils free from the carpet fibers.
4. Remove water and soils. Carpet extractors vacuum the water out of the carpet. If you are allowing the water to run off of the boat and waiting for the carpet to air dry, make sure and rinse the carpet thoroughly because the soils that you are trying to remove are suspended in the water that you cleaned with. If you do not remove that water, you are not removing the soils. You can also run push broom or squeegee across the carpet to push the water off of the boat.
Carpet cleaning chemicals usually fall into two categories.
Alkaline. Most carpet chemicals fall into this category. They rely on a hight pH to remove soils. This works because most of the soils we are trying to remove have a low pH. The chemicals that come with rental equipment fall into this category.
Oxidizers. Oxyclean is the most well known. They work by oxidizing the soils. I prefer this type of chemical because it removes organic material very well, deodorizes the carpet well and is less likely to leave a chemical residue that will attract new dirt.
I hope this very brief description helps. I'll be happy to help with any specific questions.