I just got through replacing the carpet in my Ski Nautique. I dont know about your boat specifically, but you shouldnt have any wood i nthe floor. There will be carpet on top of fiberglass held down with glue.
Pull the old carpet up, it should come up fairly easily, it will leave glue residue and pieces of th rubber carpet backing. I used a 4" scraper to get it up and it went quickly. It doesnt have to be perfect, jsut no loose material so the new glue can stick securely.
I dont like Contact Cement, it dries faster and has less room for error. Use Indoor / outdoor carpet adhesive from Lowes (Henry brand). Apply it with a notched trowel, you will have time to reposition as needed.
Use the old carpet as a pattern to cut your new. Cut it larger, but only by a 1/2 inch on every edge or so. Much bigger and you will have problems.
Do the sides first, so you dont accidently get glue on your new floor carpet while you work. Kee pAcetone and a rag handy to clean up mistakes.
Here are a few pics from this weekend of my job. The black trim at the edges was the hardest part.