Always be ready to clean glass breakage up, it will happen. Whenever anybody breaks a glass, make it your priority to get it cleaned up.
If you break a glass near ice, the chances are there's shattered glass in your ice. Throw away all of the ice.
If you spill or knock over a drink, try not to make a production of the situation. Your customer wants his drink, so clean the spillage up and get it to him, then forget it ever happened.
If you clank two glasses together, one will almost always break.
Glass doesn't agree to sudden changes in temperatures, therefore never add ice to a hot glass or hot liquid to a cold glass. The thermal shock may shatter the glass.
Never use glassware to scoop ice from a bucket or otherwise. Tiny glass slivers break off when pushed into ice, and the glass can shatter, leaving you with glass and blood in your ice. Use an ice scoop.