To begin the process of getting at your fuel tank, you need to drop your spare tire. Your Corvette's spare tire is held up under the rear of the car in a clamshell-style holder. You have a tool in your car along with the jack that you insert into a hole in the back of the clamshell to lift the tire a little while you loosen a bolt, and then you lower the lever to set the tire down on the ground.
Once you have the spare tire out of the car, you need to undo the bolts that hold the top half of the clamshell to the frame of the car. Remove the entire clamshell assembly and you can see the gas tank up under the rear end of your car.
The gas tank is held in place with a removable cross-member beam behind the differential and rear spring, and two straps that hook on the removable beam and then go around the tank and bolt into a fixed cross-member towards the rear of the car. The gas tank sits on top of the two cross-members.
Warning: Depending on the exhaust system in place on your car, you may need to remove the final length of exhaust tubing and mufflers to do this job. If your exhaust has been replaced, it may be welded into place and you might need to cut the tubes. Find a good place to cut with supports on both sides of the cut, and get some sleeves and clamps to reassemble the exhaust later.
To remove the tank, first undo the bolts that hold the straps in place. The straps will loosen, but you don't need to remove them yet. Next, undo the four bolts that hold the removable cross-member in place. Be sure to support the gas tank on your floor jack - even when it's empty, it's still pretty heavy and very bulky. When the removable cross-member comes free, undo the straps that are hooked into it.
The gas tank should sit on the fixed cross-member, and you can now work it free and lower it on the jack. You'll notice at least two (and maybe more) flexible rubber fuel lines going to hard steel tubes attached to the frame of the car. These might all be on the passenger side, or they might be on both sides of the car, depending on the year. Use your pliers or screwdriver (as appropriate) to undo the hose clamps and remove the flex lines from the car. You can leave them attached to the tank for now.