First off it depends on what type of Flyod Rose Trem system you have, if it's liscenced then what i have to say should be headed withy some caution if it's an original then this will work great for you.
1.) take a stack of your thickest credit sized cards and with the whammy (trem) bar in place, force the whole bridge up out of it's hole then slide the cards in under the bridge so that they go across the pocket where the bridge rests. Again, the cards should be placed the long way across the pocket with the width of the body.
2.) Release the bridge and let it fall into place resting nicely on the cards. Remember thick cards = more support, weak thin ass cards = "oh god no!".
3.) I usually just loosen everything, remove the string locks at the nut, loosen the strings until they can be played coherently at all and snip each one off.
4.) Restring starting at low E (6th), and progressing to the high E string (1st). Once you have all the strings in place, make sure to lock the strings in nice asnd tight in their saddles, and start tuning.
5.) Tune.
6.) Once tuned a bit over correct and or desired pitch lock the bridge and let the guitar sit for a few. Once you have it up to being tuned remove the cards, they have become uneccesary thanks to new string tension...
Anyhow that's how i do it, hope that helps you out a bit.