Cut circles smaller than three inches with a hole saw. Fit an appropriately-sized saw into a drill and set the drill at the highest speed. Mark the center of the hole on the surface of the MDF and set the pilot bit in the hole saw on the mark.
Hold the drill steady as you depress the trigger and keep it steady as the bit bores through and the saw makes contact. Let the saw cut its way halfway through the board without forcing it. Go to the other side of the board, place the pilot bit in the hole and finish the cut from that side.
Draw the outline for a circle larger than three inches in diameter on the surface of the board with a compass and a pencil. Drill a 1/2-inch hole through the material so that one edge of the hole touches the pencil mark.
Fit a high-speed jigsaw with a metal-cutting blade, place the blade through the hole and set the base of the saw on the surface. Depress the trigger to start the saw and cut around the outline, keeping the base in contact with the MDF at all times. Keep your eye on the front of the blade to make sure it stays on the line. You may have to stop periodically and brush or blow away sawdust.
Lay a solid layer of masking tape on both sides of the board that completely covers the area of the circle as an extra precaution against chipping. If the circle is very large, lay the tape around the perimeter. Draw the outline on the tape and cut directly through it. When you are finished cutting, pull off the remaining tape.