Self tanning lotion explained at howstuffworks.com. Seems it's all down to a colourless sugar called dihydroxyacetone which, as Elizabeth said, reacts with the proteins in the dead skin cells of the upper epidermis.

Useful site, howstuffworks.com, but it wasn't able to answer the other question that has been puzzling me for years - how are dodgem cars powered? Do they draw all their power from that electrified mesh above, or is there a battery in the car?