Stuff you need:

1 outdoor extention cord.
1 three prong replacement plug.
Some wire nuts.
You will also need a "mogul" (or whatever kind fits your bulb) socket.

Click the picture for a bigger view.

Cut the (male) plug end off the cord ~> Leave 12 to 18 inches of cord attached. Make sure you cut off the end with the prongs. If you cut off the wrong end & reverse them you take the risk of shocking the bejeasus out of yourself should you ever unplug the bulb with the ballast turned on.

Cut back the outer sheath- Then strip the white & black wires. Leave the green one alone for now.

Connect the wires to your mogul socket. White to white, black to black.
If / when you build a reflector for your light you're going to want to connect the green (ground) wire to the metal box onto which you mount the mogul socket.
Put it down.

Cut 4 to 6 feet of cord out of the middle- This is going to be the power wire for your ballast.

Strip the wires just like you did for the socket-
Connect them to the plug. Black to the 'gold' (or black if your plug has a black one instead of gold) screw, white to the silver one & green to green.

When you're finished it should look like this.
Put that down.

Get your ballast.
There's a bunch of wires stickin' out of the thing right? Might look a litle scary, but fear not.
Find the wires tagged "to wall". If the tag has fallen off, find a white wire with a teeny tag that says "com" on it. There's more than one- just pick any of them. Then find a black wire with a teeny tag that says "120". There's only one.

Once you've found those wires on the ballast grab the power cord you made.
Strip the other end of the power cord (just like you did for the socket & the plug) and connect the white & black wires of the power cord to the white & black wires from the ballast.
When / if you put the ballast into some sort of metal enclosure (highly reccomended, but you're on your own building that) you're going to want to connect that green wire to the metal enclosure somehow.

You should now have your power cord connected to the ballast & the recepticle part of your "outdoor power cord" connected to your light socket.
You're almost done.

Next grab the rest of your 'outdoor power cord'- the part that's got the (female) recepticle on it. Strip it's end.
Find the wires sticking out of the ballast that are marked "to bulb". If the tag has fallen off, find one white wire (marked "com") and the loose black wire coming off the capacitor.
Connect white to white & black to black. If / when you make that metal enclosure for the ballast connect this green wire to the enclosure as well.

You should now be done. All that remains is to plug the 'outdoor power cord' into itself, which effectively plugs the bulb assembely into the ballast. If you wish you can now test the whole thing by placing a bulb in the socket & plugging the ballast into the wall.

I (again) highly reccomend that you build some sort of metal enclosure for your ballast & a reflector for your bulb. This will enclose all your wiring (hopefully) keeping you from inadvertatnly disconnecting anything. It will also ground your ballast so if something goes wrong you won't get too many suprising sparks, fires or electricutions.