I don't usea fancy machine - just a wet/dry shop-vac. It's just 2.5hp, but does the job real well.
A couple of different methods.
1) For carpet mats, they get layed out in the driveway (clean asphalt). I'll vacuum, spray with a
carpet cleaner (using red devil right now, but have used bissel & others) made for machines as these don't produce suds like other soaps. If there's stubborn stains, use Oxi or Folex. Let sit for a few minutes, then work with a brush - sometime by hand, sometimes with the B&D Scumbuster. Then I hose them to get all the soap out, then vacuum to extract all the water - set asside to let dry.
2) For interior carpet I vacuum well, spray with carpet cleaner - the mix is just a bit concentrated. Then I use a small hand pump sprayer filled with HOT tap water. After spraying the water I work with a brush. Then spray with more hot water and vacuum again. If necessary, I'll spray with hot water and vacuum again.
This process is working really well for me. Of course there are always some challenges with some stains or really neglected carpet - you know, the carpet that has almost NEVER been cleaned. So these situations may involve stain removal sprays and/or the above process repeated.
Footnotes:
1) You can, but I don't think I'd use regular Woolite if thats what your doing - I believe Woolite also makes a low sudsing carpet cleaner.
2) I think you need another "rinse cycle" in your process to ensure that you get the soap out.