Huskyvacs has the right idea with his method.
The method I use to clean carpets is to vacuum first, then take a pump sprayer and fill it with hot water and carpet extractor solution, mixed as per the instructions on the bottle. Occasionally for a REALLY DIRTY carpet, I will add a scoop of OxiClean. Spray over the carpet generously, scrub in with a stiff deck brush, then use a high powered shop vac with 2 plastic wands and a Rainbow D4 rug extractor nozzle. If I want to do furniture, I have a furniture nozzle from a Bissell carpet extractor. Then spray again with clean hot water only to rinse and suck up again with the shop vac.
I would suggest NOT using powdered or liquid laundry detergent though. If not mixed in the correct ratio, it's way too easy to cause oversudsing and you will have a mess to clean up. Also, carpet extractor solutions will do a better job at removing stains if you buy a quality solution than laundry detergent will.
As for the debate over whether truckmount or portable machines are better, I tend to agree with those that say truckmount cleaners do a better job. BUT, this is because most rental or store bought machines tend to have poor suction and airflow. The ONLY WAY you're going to get a decent portable extractor is to buy a commercial grade extractor that cleaning companies use. Or, you can just buy a high powered shop vac and add your own tools. So I would invest in that first before buying a extrractor.
Rob