First, draw two lines that meet at the angle you want to bisect. Take your compasses and place the point where the lines meet. Set your compasses to any radius shorter than the shortest of the two lines and make an arc intersection on each of the lines. Reposition the point of your compasses on an arc intersection and make another arc in the space between the lines where you expect the angle bisector will roughly be. Position your compasses on the arc intersection on the other line and, without changing the radius, make an arc to intersect the arc you made on the other line. Join this intersection to where the lines meet, and you should find you have bisected the angle.