Take a new pencil and stretch elastic band such that it reaches all along the length of the pencil (unsharpened). A rubber band can also be used in place of elastic, but it will reduce the range of your bow. The pencil should be sitting snugly within the ends of the elastic band which will be attached to it at both ends.
Cut about 3 inches of tape and use it to secure the elastic band with the pencil. Cut another piece from the roll and use it to join the other end of the band. Make sure that the elastic is taut or else the bow will not work.
Stretch the elastic band away from the pencil at both ends. Elastic should stretch more on one side than the other one. Mark the side where it stretches more as this is the side you will be using.
Use a utility knife to carve out a notch into one end of the pencil. The line should be straight as it will be used to fire arrows straight in the line. Measure about 5 degrees from the straight line on both sides and mark two additional lines.
Get another pencil and sharpen its one end. Do not make it too pointy, the purpose of sharpening is to improve the flight of the arrow, and hence improve the range of the shot. Attach a plastic handle to the back of the pencil and affix it using a nail and hammer.
Put the pencil in the bow and stretch it back by holding the plastic handle. Do not apply too much force or the elastic may snap. Let the arrow fly and enjoy aiming at a board from distance.