One of the all-time great things about Corvettes is the way the GM V8 engines lend themselves to sexy side-exhaust systems. For the uninitiated, a side exhaust is when the exhaust pipes run along the bottom of the bodywork between the front and rear wheels. This design was developed early in the history of the automobile, and allows for a more direct and unrestricted exhaust system while also providing increased underbody clearance and less heat transferred into the cabin.
With any engine, de-restricting the exhaust path is an easy and simple way to increase horsepower and torque. Simply put, if your engine doesn't have to use power to push the exhaust gases out the back of the car through a narrow and winding passage, it can use that power to drive the car instead. So, with certain caveats, a free-flowing exhaust is better than a restricted exhaust. However, there are those caveats. The first being that if the exhaust is too free-flowing, you won't get as much velocity in your exhaust gases, and that velocity helps with high-rev horsepower. The other caveat is that headers and side exhausts tend to be much louder than stock, and this can get you in trouble with the police - check your local laws! Also, if your Corvette was made after 1975, you need to think about your catalytic converter.
But if you want to put headers and side exhaust (side pipes) on your classic 'Vette, you can follow the steps in this article. Be aware that it involves cutting your bodywork on C3 (68-82) Corvettes!