A peltier is an electrical device. When electrical current is applied, one side gets hotter and the other side gets colder.
For cooling a CPU, you would go in this order: CPU>thermal grease>copper heat-spreader plate>peltier>thermal grease>high-capacity heatsink or water block. The heat spreader is important in order for the whole cold side of the peltier to get thermally connected to the CPU. If the heatsink can't handle the heat load of the CPU plus the peltier, then you're in trouble.
Since the cold side of the peltier element may cause water to condense from the air, you would need to seal off the peltier from the surrounding air also. The peltier may draw enough power to require a separate power supply too, perhaps an old AT power supply which turns on with a switch.