Drive out the old rivet pinning the fork to the handle with a hammer and punch. This hollow part of the fork where the handle is fitted is called the tang.
Measure the distance from the crossbar, or shoulder, of the fork to the rivet hole in the tang.
Insert the new handle into the hollow of the tang. Set the grip against the floor so you can tap the fork's crossbar with a hammer, ensuring a snug fit.
Mark the rivet hole by dabbing a marker through the hole and onto the handle on both sides of the handle.
Remove the handle from the fork, double check the marked holes using the measurement from Step 2 and drill a hole straight through the handle from the mark on one side to the mark on the other. Select your drill bit so it is the same size as the replacement rivet.
Put the handle back into the fork, set the grip against the ground and tap it back into place. Make sure the holes in the handle are aligned with the holes in the fork, and place the fork against an anvil, steel beam or something similar. Insert the rivet and pound it with a hammer until the top and bottom of the rivet have flattened out, locking it into place.