1) Tune a Floyd
The Floyd Rose is a floating bridge. It is not fixed to the body, but rests on two poles. The balance is achieved by countering the string tension with springs. This brings to the rule number 1: unless you have A LOT of experience, do NOT change the string gauge by yourself: the tension will change and your neck will suffer.
The Floyd system has two units: the bridge itself and the locking nut. The bridge locks the strings too, that is why a Floyd and its many licenced derivatives are considered a double locking tremolo. It ensures tuning stability after abusive use of the whammy bar. Judge by yourself: My licenced cheapo Floyd is 17 years old and stays in tune PERFECTLY even after a good dozen of full divebombs.
But of course there is a pay off: The bridge has to be stabilized all the time you tune and it's a hassle. This means that Floyds don't like alternative tunings. Each change in tension in one string changes the tuning of others.
Make sure you clip out the ball ends. They won't fit the Floyd. Or else put them through the machineheads but it looks ugly :P
Ok... so your strings are on the guitar, they are stretched though not tuned? Now you need to tune...
1) ensure the strings are properly locked in the bridge. Use an allen key to tighten them if necessary. (I'll add pictures later)
2) that's when problems start... People have different ways of doing it. I mess about a lot with the spring tension at the back so tuning is also done differently taking care of this. Let's just assume the spring position, string gauge and wanted tuning are constant. The way I do it:
Usually the locking nut is unlocked because the fine tuners don't have such a big range. I tune my low E to proper pitch using the mahineheads, then I do the high e, then A, then B, then D, then G. And I repeat it. All the way. Usually it takes 3 to 4 times doing this. When the guitar is in tune, I simply lock the nut and use the fine tuners to finish.
You want to drop D?
Some people would unlock the nut for the E and A strings, drop the E, lock again, fine tune and here you go. Well unfortunately... Your strings will still be relatively in tune with each other, but they won't be perfectly in tune.
As Damage mentioned, open tunings really won't work well. I wouldn't try them. I haven't yet myself. I usually keep mine in E standard but right now it's in Dropped C. Here's what I had to do (it still is tuning. Tune with the locking nut unlocked, and when you lock it again, fine tune)
1) I tuned all the strings a full step down.
2) I slackened the spring claw at the back to re-establish balance
3) I tuned again
4) I slackened again. By now the bridge should be in the position you want it. It may take more, depending on how you do it and how you want it.
5) I dropped the D, and tuned it all over again a few times until it was perfectly in tune.
A word on springs
The more springs the more tensions. People most often use 3 springs in a ||| configuration. Next comes the /|\ configuration. It makes bending the lowest and highest strings a little easier. To be honest, I didn't notice much difference.
Some people use 2 or 4 springs. I don't see why not. But to me, 3 springs is perfect.
Oooooook I think that's it. To everyone who say that Floyds are a hassle: I have just started playing guitar. This guitar pictued here is my first electric guitar. I never had a problem with the Floyd. You just have to know what you're doing before getting one, or learn about it before tweaking it.
Though you do have to be patient