Whatever device you use to cut it should be sterilized first if possible. If all the blood has clotted in the cord before cutting, you don't technically need anything except something to cut it with (scissors being the easiest option--but candles, a knife, etc. can work too).
Sometimes they can get oozy afterwards. For security's sake, I think it is best to use something to help prevent the oozing from becoming full on bleeding. You can use shoelaces, cotton cord, yarn, plastic cord clamps, or elastic bands to secure the cord. For ease of explanation, let's pretend you use shoelaces...
Tie one shoelace tightly around the cord a few inches away from the baby's navel. Following the cord up to mom, leave an inch or so of space, and then tie another shoelace around the cord. Now you have two areas where the cord is tied with a bit of space inbetween the two ties. Cut the cord in that space between the ties.
You do not need to use anything (rubbing alcohol, hydrogen peroxide, iodine, soap, etc.) to clean the cord afterwards. Just leave it alone and it will fall off / heal on its own.