Order a replacement handle from the manufacturer. If you cannot get replacement handles directly from the manufacturer, try a local or online specialty store. Although they may not have the exact handle you were looking for, they may be able to produce one that will work.
Unscrew the screws in the plastic around the handle on the top of your piece of luggage. You may need to go inside the liner to find the hardware for you handles. The number of screws will depend on the manufacturer.
Follow the shafts of the handle to the bottom of the bag. Find the screws in the plastic piece on the bottom of your luggage that holds the handle in place.
Take out the screws going into each shaft of your handle.
Remove the handle and switch it with the new replacement handle.
Push the handle all the way down to the bottom of the luggage and replace the screws in the shaft.
Re-position the top plastic piece on the top of your luggage and screw it back into place.