I've done my own a few times using a rental machine from the local super market.
If you decide to go this way follow the instruction to the letter. Don't be tempted to add any extra cleaner.
I used hot water in the tank and that seemed to make it easier. You'll be surprised at the amount of muck in the water
What I do is...
1. Do a really good vacuume first.
2. Clean the skirting boards especially the tops.
3. Setup the machine and chemicals etc.
4. I start in the main traffic areas first and get this as clean as I can.
5. Then the rest... As I push forward I press the trigger for the spray. Then pull back sucking up the same area.
You can leave the spray on/in the carpet for a bit longer in problem areas.
Go slow and you'll find your own way of doing it and you'll soon be in a hypnotic Zen like state. No joke... I actually look forward to that part.
When done put down some clean towels so you're not walking on wet carpet. It will take a few days before it's 100% dry.
The pros do an excellent job but they won't take the time to concentrate on the problem areas like you can.
Usually I hire the machine for a whole week end and take turns with my GF. While she's using it I'm getting the next lot of water/detergent ready and visa versa.
I pour the dirty water down the toilet rather than in a sink.