Position a straight edge that is long enough diagonally across the door's middle rail, extending from corner to corner. Mark a line on the door -- using the straight edge as a guide -- that crosses the middle of the middle rail. Use a pencil to draw the line.
Switch the straight edge to the opposite corners, positioned diagonally across the middle rail. Mark a similar line on the door across the middle of the rail, using the pencil.
Install a 3/16-inch drill bit into a power drill. Drill a hole through the spot, using the drill, where the two diagonal lines intersect, which marks the center of the middle rail. Drill the hole completely through the door.
Insert a screw through the hole, from the interior side of the door. Hold the screw head steady, using a Phillips screwdriver, and thread the doorknob onto the screw from the other side of the door, until the knob is tight.