renting a carpet machine is last resort.. I worked at a detail shop for a few years during high school and we used the same soap you'll but at walmart or autozone (turtle wax carpet cleaner) and then we sprayed a good layer down. Then we scrubbed it down well..
Right but before you do anything make sure your trucks 100% clean, meaning dust, dirt, anything from dash boards, center counsel, door panals etc.. I say that because It will just make it easier after you finish, your carpet and your car will be clean.
Give it a good vacuum, while removing as much crap from the carpets as humanly possible.. A good shop vac with the detailing attachments will do good.. the Attachments are 20 bucks at home depot.
After you've vacuumed go over it once more just to make sure you got everything, then spray down the stuff (buy a couple bottles) lay it thick let it settle a for a few minutes then go at scrubbing it down. Normal areas can get by with a moderate scrub but heavily dirtied areas will need a good scrub.
with the carpet cleaner do one area at a time and make sure you get under the sear as much as possible. meaning move them back and forth.
after you've finished an area vacuum up the area and move on to the next..
Between the seats and the carpet should take you a good hour or more depending on the condition.. and wiping down the car should take no more than 10 minutes.
Make sure you wear rubber gloves, me personally I hated how my hands felt and smelled after cleaning the carpets.
You might have to do an area twice, but that is just how it goes with carpet that isn't black. After you've finished, ponder purchasing all season mats that will protect the carpet from everything. Something we always recommended.
Your car doesn't look that bad from your picture, I've definitely dealt with worse.
Good Luck, have fun, make a good play list