Okay, adding some more content that I had previously posted.
The carpet in my 79 Trans Am was pretty shot so here's some pics and comments about the installation process. I eventually changed the seats to Procar Rallys and have the rear seat covers on order with Procar, but they have been on order for nearly 6 months...
The carpet I used was ordered from Stock Interiors (8835-Medium Beige Plush Cut Pile). The quality is decent, but it does tend to shed. I would probably choose a different cut next time around.
Overall this a pretty easy installation, but takes some time to make it look clean. As far as what will need to be removed, here's what I can remember but there may be a few more pieces - seats, doorsill step plates, center console, seat belts, carpet (obviously), and underlayment. Cleaning off the old underlayment can be a huge pain and will leave you pretty grossed out if your car is in as bad a shape as mine.
While you are getting everything out of the car, make sure to lay the new carpet out to get the packing folds out and make installation easier. I hear that doing this in the sun or leaving the carpet in the sun to make it more pliable makes it easier, but it was not really necessary.
As far as underlayment goes, I used Cool It, but there are lots of choices with varying levels of sound and heat suppression so do a bit of research here. The key to get good coverage with whatever you go with. And careful here as the edges of the material can leave your fingers with lots of papercuts. Ask me how I know.
Its a good idea to keep track of where the seats and seat belts bolt down as you lay down the underlayment and carpet by marking them with tape or cutting slits. Also, you are going to need to trim some of the carpet, most likely the sides by the doorsills. Cut a little bit at a time. you can always cut more but cant put some back if you cut too much.
If you are planning on running new speaker wires or installing a new head unit, now is a great time.
Take your time and have fun with it.