** How do I stop a squeaking drum when the dryer is running? **
As Tom stated, it will depend on the dryer's brand and possible the model number off it too. You can read tips for locating the model number on your appliances in the 'Repair Parts' section of my site linked below.
Possible causes include worn front drum slides (if used on your model), worn idler pulley, worn drum rollers (if used on your model), a worn rear drum bearing (again if used on your model) or bad motor.
I disagree about the belt being a possible cause. Belts used on appliances do not usually make a squealing sound like that can on automobiles.
Whatever you do, don't go crazy trying to oil anything or spraying automotive 'belt stop squeak' on the belt as neither will solve the problem and may cause further problems. Fix it once and fix it right!