Although you may be tempted to just wrap an old shovel handle in duct tape or buy a new shovel when your handle breaks, you should think twice. Using duct tape on a handle is dangerous. While the tape may hold up for a short while, eventually it will tear, and you will have the same broken handle as before. Using a cracked or broken handle is also dangerous, and replacing a handle is simple.
Examine your shovel handle carefully. Measure the length and note the direction of the grain. While some modern handles screw onto the head of a shovel, most shovel heads are riveted in place for greater stability. If your shovel's handle screws onto the head of the shovel, simply purchase a handle with a grooved end and screw it into the shovel socket. If the shovel handle does not screw into the socket, purchase a handle at a hardware store and have it cut to the correct length. Purchase a handle with the grain of the wood running the length of the shovel.
Fit a grinder bit into an electric drill, and grind the heads out of the rivets that hold your broken shovel handle in the socket of the shovel head. Place a punch against the rivet, and drive it out of the channel made by the socket head and broken handle with a hammer.
Pull the broken handle out of the shovel head's socket. If the handle is broken off inside the socket, switch the drill bit head from a grinder to a Phillips head bit. Drive a wood screw into the broken handle. Clamp the screw head into a vice. Hit the shovel head with a mallet to loosen it from the broken piece of handle. Then pull the shovel head socket off of the handle.
Sand the end of the new handle to taper it to the point so it will fit into the socket of the shovel head. Tap on the end of the shovel head to seat it. Drill ¼-inch pilot holes into the handle through the rivet holes in the socket. Then drive wood screws into the pilot holes.