"Sometimes they save your life, sometimes you might as well paint a target on the front of 'em"
The bullet that hits the shield passes through and hits the player, and the player takes damage as usual,
The shield absorbs all the damage from the bullet, but the shield is damaged in the process and discarded. You may take the shield to a Mechanic with the Repair/Build Item skill to get it fixed.
The player who's shield is his decides which of these options to use at the moment of damage and should respond appropriately. Note that this only applies to damage caused by firearms; bows, melee weapons, etc do not damage shields without using special calls.