Snap a chalk line across the driveway where water puddles after it rains. Snap a parallel chalk line about 8 inches apart from the first line to outline the path for the drain pipes.
Saw along the chalk with a wet saw if the pavement is concrete or asphalt. Break out the outlined section into smaller chunks with a sledgehammer and pry off the pieces with a pry bar. If the driveway is sand-set with pavers or bricks, pry off the bricks with the pry bar.
Remove the foundation gravel and dirt to dig a channel 1 1/2 feet deep with a shovel. Create a slight slope from the higher side of the driveway to the lower side.
Dig another channel 10 inches wide and 1 1/2 feet deep against the side of the driveway. Slope the channel toward the driveway by at least 1 inch for every 8 feet of distance.
Pour 8 inches of clean gravel in both channels and shift it into a slight slope with a rake.
Place a 4-inch wide PVC perforated drainage pipe at the center of the channels running through the driveway and down the side. Attach the perpendicular pipes with an elbow connector, and screw a drain grid over the open end.
Fill the remaining channel running across the driveway with clean gravel until it is 3 inches from the surface and has a 6-inch layer of gravel over the pipes along the side.
Smooth a 1-inch bed of course sand over the gravel running across the driveway.
Position bricks on the sand bed so the sides are flush against each other and adjust the sand bed as necessary so the bricks are level with the existing pavement. Fill the gaps between the bricks and pavement with fine sand. The result will be a row of bricks across the paved driveway. Bricks will help wick some moisture, mask the drain and provide visual contrast to the existing pavement.
Fill the rest of the channel along the side with dirt and plant Bermuda grass or another flood-resistant groundcover over the dirt.