Basically it works on the principle of thermo-electric effect (opposite of Seebeck Effect) where a potential difference is used for making or producing hot and cold temperatures over the two ends of a dissimilar metal assembly.
The application of voltage instantly starts transforming one surface of the unit hot and the reverse surface cool very fast.
However, the hot end must be quickly managed so that the heat does not reach higher levels, which can completely hamper the heating and cooling process and ruin the device itself.
Therefore the hot surface must be attached with heavy heatsinking materials like aluminum or copper metal of suitable sizes.
The simple construction of a simple peltier refrigerator circuit shown in the figure demonstrates the above discussed set up where two such devices are appropriately fixed with aluminum plates for radiating different degrees of temperatures from their relevant sides.
The plates responsible for generating the cooling effects must be trapped inside a well insulated enclosure made up of thermocole or polyurethane foam etc.
The inside chamber may be used for storing water bottles or water packets as desired.
The hot heatsinked surfaces must be exposed in the outside air for radiations and for controlling the temperatures of "hot" ends of the unit, see figure.
Complete diagram for understanding How to Make a Simple Peltier Refrigerator at Home.