Purchase a replacement handle. Replacement parts may be ordered from several websites or from the manufacturer. Make sure to get the correct handle for your make and model of suitcase.
Remove the screws from your broken suitcase handle. The handle usually has two screws at the top and two screws at the bottom. Set these aside, and remove the old handle from the suitcase.
Insert the new handle into the suitcase. Replace the screws you previously removed. Extend the handle and apply a liberal amount of WD-40 or other lubricant. Extend and retract the handle a few times to distribute the lubricant evenly.