I grew up with clean rugs. My mother washed them often. But she did not have a carpet cleaner or a Big Green Machine and she certainly never hired a professional to come in and clean the rugs. No, she washed them... with a MOP!
Start out by vacuuming your rugs. Then put some hot water in a bucket with a bit of ammonia (see the ammonia bottle for suggestions as to how much ammonia to add).
Soak a clean sponge mop in the water/ammonia solution and wring it so it's not dripping, but leave it fairly wet. Then just mop your carpet like you would mop a floor. Change the water in the bucket often so you are not just spreading around more dirt.
When you are done mopping your carpet and rugs, just let them dry. If you need for them to dry quickly, you can lay blankets on them and walk on the blankets (or let your kids run around and roll around on the blankets like I used to!). When the carpets are dry, just vacuum them again to suck up any lifted dirt.
Keeping your carpets vacuumed and washed really extends the life of the fibers. My mother took much pride in how nice her carpets looked... even if they were 30 years old and WAY out of style!!! I have since ripped out all the carpeting, including the orange/gold/brown marbled shag carpet in the dining room. Yes, it was in great condition... but it was UGLY!!! (sorry ma!)