Door gaps, especially on exterior doors, can be serious energy wasters. In the winter they let cooler air in, and in the cooling season when your air conditioner is running, they let cool air out. If you have individual heating and cooling for each room, the same situation applies for interior doors too. However, unless you want to raise the entire floor beneath the door, there are ways to close the gap that are do-it-yourself methods and are cost-effective.
Screw on a door sweep. This is done from inside the home on an exterior door, and the sweep will effectively block the gap under the door. There are several types available, from an actual bristle-type sweep that hangs below the door and blocks the gap, to rubberized types that bulge slightly to fill the gap.
Measure the width of the door and transfer that measurement onto a door sweep with a marker. Put on a pair of safety glasses and cut the sweep to length with either a hacksaw or a jigsaw. Place the sweep at the bottom of the door and align the sweep edge so that it blocks the door gap. Make marks through the pre-drilled attachment holes onto the door proper. Pilot hole the marks with a drill and drill bit, then insert a screwdriver bit into the drill and screw the sweep down through the drilled holes. All sweeps will come with mounting screws for ease of application.