Which I think is 6.6v/.75A which the arduino can't handle. I've got a 12v power supply but I am not sure if there is an elegant solution to use that to drive the Luxeon. (I have a 7805 Chip, LM340T5 that someone else said would work but analog components are still very Greek to me, heh)
I'm also not sure how to put a switch into the line, relay?
A relay would work. You will need to limit the current supplied to the led though. Connecting a relay to your arduino, probably, isn't as straightforward as you're hoping.
For simplicity I'd suggest something like:
Which has plenty of headroom in case you want another Luxeon.
No it doesn't, you should still design it as if it were on all the time for the purpose of voltage and current. The fact that you pulse it means the power dissipation is reduced and so you might not need as big a heat sink.