i am at the same level of ignorance as you im afraid, i was also trying to control fan speed with a relay, then i googled a bit and found a page similar to this ,
http://bildr.org/2011/03/high-power-control-with-arduino-and-tip120/
that page is a good one to help understand how to connect it all, i didnt use a tip120 though, i just grabbed an old transistor from the parts box and tried it out,
what you want to make sure of is that the transistor can easily handle the volts and amps needed , with a good margin, otherwise it will get hot and you will need a heatsink, i would use a heatsink anyway though