PEltier tile science fair project
The normal way to identify the hot and cold side is to connect the Red(+) and the Black(-) leads of the peltier module to an Alkaline AA cell for 5-6 seconds. You should feel one side become warm and the other side cold. Mark the hot and cold side. Its just that easy. As for a mot spinning the current output from a Peltier module is very low."I hope you haven't connected one of those brushed motors!". You could use something like low current device like a 12V 0.1A DC fan?

Also what is the model of the Peltier that you intend to use?

You should apply thermal past to the hot side and fix the heat sink on the hot side.I would suggest yo use a aluminium thick plate there instead of heat sink. Since its to absorb the heat.