Ok here goes, first are machine process:
Typical extraction method, pre-treat with APC+, extract, rinse, repeat. Standard stuff, but I can get into more detail if desired.
Steam method, pre-treat with CG Fabric Clean, Diluted 1:16, using steam nozzle, steam 1-2 foot section, thoroughly agitate with MF towel or brush, then wipe with separate MF towel, horizontally, then vertically.
Manual method 1, my most used process by hand. Evenly mist entire section of carpet with CG Fabric Clean, agitate with brush or MF towel. Let sit for 1-2 minutes, more if the temps are low. Mist again with FC then wipe with clean, dry MF horizontally, then vertically.
Hand method two, bad carpets. Start with APC+ 1:10(even 1:4 can be used), thoroughly spraying entire section until "damp". Agitate then let sit 5-10 minutes. Vacuum(this pulls any debris out of the carpets that your agitation loosened). Mist with CG FC. Wipe thoroughly horizontally, then vertically. Change MF's. Mist and wipe again.
Hand method three, abandon all hope ye who enter. This is for really bad carpets only, and there is little chance the carpets are going to look good, you are just trying to get them clean and debris free.
1. Strongly spray with APC+, agitate, vacuum.
2. Use a strong foaming cleaner, like Tough Stuff(this is actually a very versatile product). The reason is that the foam is going to "lift" a lot of debris out, and will help kill any bacterial issues that the APC+ did not take care of. It is also a decent stain remover. When I say foam, I mean you are using most of a can on just one vehicle. Again, these are really bad carpets. Let sit 15+ minutes and dwell. Just make sure the carpets don't completely dry. Agitate then vacuum.
3. Mist with CG Fabric Clean, wipe horizontally, then vertically, rinse and repeat as long as you are getting results. Know when to call it quits however.