You need a 12v DC power supply for the coil. The wiring is fairly simple. Coil is contacts 13/14 with 14 being the positive. Hook you 12v negative to terminal 13 and your 12v positive connects to one end of the float switch, while the other end of the float connects to terminal 14.
For your 120v AC, you can use either of the two points. Don't switch the neutral wire on your extension cord. Just cut the hot wire and run it through the relay. Neutral will be the larger blade on the male end.
One set of NO points is terminals 12/8, the other set is 9/5; you can use either one. Just connect the hot on the extension cord to either of those pairs of terminals.
I would highly recommend that you mount all of this in a small project box.