Look at the top, non-pointed end of the bob for a hole. This may be in a small handle at the top or in the top of the bob itself. Look around the sides of the bob just underneath the top for a second hole. You might not see one, depending on the model. If you do, skip to Step 3.
Try twisting the ends of the bob to separate them if the bob appears to have two pieces screwed together. Unscrew the two halves completely.
Insert one end of the string into the hole. Grab the end of the string with tweezers or lance it with a pin to pull it through the hole. If the bob doesn't unscrew and has holes in the side just under the top, push the string down with the pin and tweeze it out through the second hole.
Tie a large knot in the end of the string. If the string is a nylon cord, you can also melt the end with a lit match or lighter. Touch the end of the cord to the flame very quickly. The nylon will melt and form a ball. Repeat until the ball is big enough so that it won't slip back out the hole. Wait a few minutes for it to cool down. If the string is hanging out of a side hole, you want the knot to slip back inside the side hole, but not the top hole.
Cut off any excess string hanging past the knot.
Test the knot or ball by pulling the string tight. Ensure the plumb bob isn't going to slip off the string. Do this with the bob held right over a surface, preferably a soft one. If the bob does slip, the bob will fall only a couple of inches, and the point won't be damaged.
Screw the second half of the bob back on, if appropriate for the model.