Draw a pattern for the hole on a piece of paper. Use a compass to help you get a perfect circle, if necessary. Cut out the pattern and trace it onto both the outside and inside of the bookshelf, measuring to ensure the two line up perfectly.
Cut around the perimeter of the pattern with a bench knife. Use a gouge to make a series of stop cuts around the inside perimeter, flaking off wood by cutting diagonally toward the pattern line. Continue until the border of the circle is carved so deep that the wood is less than half as thick as it was previously.
Repeat Step 2, this time working from the outside. Eventually, your stop cuts will break through the surface to the other side. Continue working around the perimeter until the wooden disk in the middle falls out of the hole.
Soften the perimeter of the hole with a straight chisel, evening out the surface. Sand the edge of the hole smooth.