Tuning is often overlooked. It's an art and a science,imho. With a Floyd, you'll need a little sorcery thrown in..
This is what I teach my students:
1. Buy good strings (I prefer D'addarios...they are American made and the QC is very high)
2. Always put them on a week before you need to gig. Never shorten this!
3. As you take each old string off, put the new one on...
example: Remove the old low E and then put on the new Low E..now go and do that for the A and D etc etc
this maintains tension on the neck and springs and it's wise for many reasons more,as well.
4. Keep the locks on the neck slack all during this:
Once the strings are on, at the 12th fret pull the strings one inch off the fretboard. This stretches them in. Your hands are clean, right? Good.
Note: Take it easy on the high E and B strings with pulling. In their case pull 1/2 inch, not a whole inch and as they are really prone to slipping off their posts.
5. Using a good tuner: Tune it first to Low E D G A B Hi E then repeat. each time the guitar will get a little closer to being "there". Still do not tighten the necks' lock.
6. Play the guitar for about 3 days like this. Bend all the strings often, this will "let out" whatever tension the strings are holding. Because the locks on the neck are loose be careful they dont fall off. maybe put em in the case for the next 3 days.
7. After three days tune again (using an accurate tuner), like before, EDGABE is the order.
8. Now lock the neck down, and have fun.
This works very well. But you can't rush it.
I have my Floyd Rose-guitars set so I can pull up, as well as down. I can pull up as much as a 5th (!!!) and stay in tune. That's from an G at the 12th fret to a D note above. And I stay in tune, almost always.
Like I said, I teach guitar...if you like what I know ,and live in Long Island area, consider taking lessons from me. What I know sure beats trial and error! -George Barry (GtrGeorge!)