To install a culvert into the driveway, cut through the concrete using a concrete saw, remove the concrete, and create a trench for the culvert. Cover the bottom of the trench with gravel, place the pipe on it, cover it with more gravel, and fill the trench with dirt. Make sure that the culvert is working, and repair the concrete layer on the driveway.
Before beginning to install the culvert, find out if you need a permit for this work. The local building code enforcement should have all the necessary information about regulations and the process of obtaining a permit. Sometimes, there are regulations on culvert pipe characteristics, so find out all the information before purchasing a pipe.
When buying a pipe, measure the length of the driveway, and buy a pipe that is a little longer than that, as the pipe should extend past the driveway to make sure that water doesn't collect at the end of it. Use 6 to 18 inches of backfill below the driveway to protect the pipe from getting damaged by cars.
Use chalk to draw an outline for how you are going to cut the concrete. Draw two lines at least 1 1/2 times the diameter of the pipe. Use a gasoline-powered concrete saw to cut the concrete. Always wear goggles and protective clothes when cutting concrete.