Need some help with wiring

I am having a little trouble understanding how to wire up my stir plate, I've seen plenty diagrams I'm just not sure how to apply them to what I'm doing. I have a 12v power supply that is AC but I believe it has a DC adapter (Its a little inline plug?) and a 12v computer fan. I also want to wire in a 3 led light from a fountain that the power supply came from. I will probably need a resistor for the led's and a potentiometer or something for the fan so how would I do this? I don't want the potentiometer to affect the led's nor the resistor to affect the fan. I'll try to post some pictures of what I'm working with.

This is my 12v ac power supply, led, and fan. Seems simple enough.