I removed the carpet, hosed it down, spot treated with Folex, hosed it down some more. Used a shop vac to soak up everything I could. Continued to spot treat, and do lots of scrubbing using Folex. Once I was content with how clean it was, I used a shop vac again to soak up everything I could. I then let it sit in the sun for 4-5 hours to completely dry, and reinstalled.
When you're just putting the stock carpet back in, there is no glue required. Just put it back in, put all the seats/center console/molding back in, and it'll look like it never came back.
Carpet for coupes and sedans are the same. At least every year 97-03 is the same, I don't know what might be different in 04+.
As far as cutting/trimming: Lay out the new carpet next to, or on top of the old carpet if you need a guide on where to cut.