Measure across the width of the sink along the back of the counter top with the tape measure and mark the center of the sink with the grease pencil. Consult the faucet manufacturer's instructions for the distance between the faucet supply lines. Divide this distance by two.
Place the ruler with the mark on the counter top indicating half the distance between the supply lines on the ruler. Make a mark on the counter top at the end of the ruler. Make a third mark on the opposite side to indicate the second faucet hole without moving the ruler. Measure between the two outside marks to verify the distance is the same specified by the manufacturer.
Check the faucet manufacturer's installation directions to find the hole size required for the sink. Install the correct size hole saw in the drill.
Place the point of the hole saw's pilot drill on one of the outside marks and keep the drill vertical. Start the drill and increase the speed to a moderate setting. If the speed is too fast, you will burn or melt the counter top. Let the hole saw make contact with the Corian and apply light downward pressure. Let the saw do the work.
Continue cutting until the hole saw cuts completely through the Corian. Stop the drill and remove the saw from the hole. Use a screwdriver to pry the cut piece of Corian out of the saw. Cut all the holes required by the faucet in the same fashion.