I believe that the flash output is controlled by the length of time the flash is fired...but we don't normally refer to it that way. It's more typical to use the factions of full power. For example, if you fire the flash at 1/1, it's full power. If you go down one stop, it's 1/2...one more stop is 1/4....one more is 1/8 and so on.
The actual power/output of the flash is given by it's Guide Number. In this case, the Guide Number of the 430EX is 43 meters (at ISO 100 and full zoom).
The unit’s guide number (provided in metres, not feet, for ISO 100) varies depending on the zoom head settings.
# At 14mm (with the flip-down diffuser in place) the guide number is 11.
# At 24mm the guide number is 25.
# At 28mm the guide number is 27.
# At 35mm the guide number is 31.
# At 50mm the guide number is 34.
# At 70mm the guide number is 37.
# At 80mm the guide number is 40.
# At 105mm the guide number is 43.
You can use the GN to calculate exposure. GN divided by distance gives you the aperture value for proper exposure. So at 80mm (GN of 40m) if the flash is 10 meters from the subject, you need to use an aperture of F4.
I understand how to use the power options but am not as confident about the focal length. Do longer focal lengths "focus" the light at a further distance?
Sort of, yes. The 'focal length' on the flash is basically a reference to the field of view that a lens of that focal length will have. When on the camera, the flash zooms the head so that the spread of light matches the field of view of the lens. This makes it more efficient because it's not lighting areas that can't be seen by the lens.
So given that the flash bulb/tube fires at a constant power, by zooming the head, you concentrate that light into a smaller beam, thus giving you more reach (higher GN, more light).
When using the flash off-camera, it can be fairly useful to change the spread of the light to suit your needs. It's almost like having barn doors on a studio light, in that you can control the angle of light spread from the flash. But with the flash head zooming, you also get more output as you tighten the spread.
This is important to think about in terms of placing your flash. If you are using a wider spread than you need, you are giving up working distance. In other words, you can get more working distance out of the flash, by zooming the head to get a tighter beam...just make sure that you aren't going too tight for the lighting effect that you want.
Assuming my assumptions are correct, how do you navigate these 2 options to correctly compensate for exposure without guess and check?
You could use a flash meter...but I think that most photographers tend to pick this stuff up with experience. After a while, you tend to get a feeling for what aperture you need to use when you flash is at 1/4 power and 10 feet away from your subject. If it's not quite right, you can adjust the power and/or move the light closer or farther from the subject. If your initial guess wasn't far off, it shouldn't take long to make those adjustments.