There are many reasons you might want to replace the carpet in your vintage Corvette, including restoration to factory original specs, but the main reason to replace carpet is usually that it has gotten wet and mildewed, or mice invaded your car and stunk it up, someone once put house carpet in it for fun, or it's just too shredded for continued use. But no matter what the reason, you have to get that old carpet out of the car before you can put in a new carpet kit.
While you're thinking about pulling out the carpet, it's also time to order up your replacement carpet kit. Any of the big online Corvette stores will have it, and you can often find a good kit on ebay and save a few bucks - but remember that on ebay you're kind of taking your chances with the fit. The Corvette stores have to stand behind their products so they tend to be better kits. Order the carpet for your year and specific Corvette model - in some years the kit is different for manual vs. automatic cars, and of course, different for convertibles vs. coupes.
You will also want to make sure you get the right color code for your car.
For some years of Corvette, you'll have a choice between loop carpet and cut-pile. Loop was the basic interior on base model cars for many years, while cut-pile was offered as an option. Later cars all use cut-pile. Personally, I like loop carpet better as an indoor-outdoor kind of material well-suited to cars, but the choice is up to you. Just note that if your car came from the factory with loop and you upgrade to cut-pile, you could lose concours points for the change.
When your carpet arrives, take it out of the box and lay it out. You want to give all the creases a chance to relax so the carpet lays better when you install it in the car. Leave it out (preferably in a warm place) for a few days before the installation. This also gives you a chance to take a good look at it and notice any potential anomalies.