karolra10- Hot water/chemicals work better than cool. Some stains respond a lot better to certain products than they do to other products. Some carpets are more fragile than others.
Some stains simply won't ever come out.
I prefer to use pro carpet-cleaing products instead of APC, but sometimes I'm working on carpets where I don't want an "oops!" so maybe I'm erring on the side of caution.
Note that the smaller the opening in the wet/dry vacuum's nozzle, the easier it is to get more moisture out.
All-in-all it's not too different from cleaning the carpets/rugs in your house.
Note that David Fermani does his (*VERY* impressive!) carpet work *without* an extractor/wet-vac! It might be worth the dreaded search (or something..) to check out how he does it...primarily a matter of using cotton towels IIRC.
EDIT: Oh, and Welcome to Autopia!