First of all, when changing the strings, make sure you take off one string at a time and replace it with the new string before you take off another. If you take off all the strings at the same time (like so many first time Floyd Rose owners) you'll have to remount the entire bridge. (which is a total pain in the ass)

The best advice I can give concerning tuning is to tune the whole guitar up to F or F# and let the strings stretch out. Let it sit there for about an hour and then go tune normally. Also, a lot of people start their tuning at the low E string. This will always cause problems because the low E string, being the fatest, has the most tension on the bridge. Start at the high E string and tune down using harmonics.