The camera's synch terminal, either on the hot shoe or a separate connection is the way to synchronize the flash to the shutter. Assuming that you DO NOT want TTL control of the flash output, then you can adjust the output of the LED by pulsing it on for a varying duration. Let's say 1/10000 second is the low power setting, then 1/1000 second could be a high power setting. There won't be a linear relationship - you'd have to use trial and error to figure it out. A 555 timer IC in monostable mode driving a transistor switch can work (see the first link below). The thing about pulsing a LED for very short durations is that they can take a lot more current - ie: They'll be a lot brighter. Something like 300% of their maximum rated continuous current according to the second article below.
So, the camera's synch terminal is just a switch. This is used to trigger the 555 monostable to produce a single short pulse which turns on a transistor switch which turns on the LED (via a resistor to limit the current to a safe level) for the duration of the pulse. The pulse is short - 1/10000 second say. A resistor and capacitor in the 555 circuit determine this duration.
Camera's usually synch at shutter speeds from 1/60 second to 1/250 second - so much longer than the flash pulse.
http://www.electronics-tutorials.ws/waveforms/555_timer.html
http://www.cree.com/~/media/Files/C...Lamp Application Notes/XLampPulsedCurrent.pdf
This should whet your appetite for now. Come back when you're a bit further along...
And don't forget there are LOTS of commercially available LED flash units - if you get stuck... or want something that works straight away. And XENON flash units are very cheap too - (esp if you can get hold of those old disposable cameras with flash).
