Stole this from another site, not quite my way of doing it, but probably simpler……spelling mistakes are not mine……..

Robert’s note: It all becomes much easier if you put the uncut string in from the headstock end, leaving the ball hanging from the tuner. You can cut it after you’re done, and it also prevents any slippage of the outer wrap on the wound strings.

Discussion on this here: https://www.facebook.com/freyaguitars?ref=hl

Floyd Rose restringing
This is the way I re-string my Floyd’s. Extra note, I clean them at the same time.

1, using the card from the new strings, block the trem so it can’t pull-back into the rear-route.
2, undo locking nut.
3, put the micro-tunersso there’s no tension on them.
4, undo the sting clamps on the bridge.
5, clean the guitar (I always do this when changing strings)
6, one string at a time, snip the ball-end off and clamp the string into the appropriate holder. NO need to go stupid with the tightness of the clamp, just nip it up.
7, tighten the string with the machine head ubtil almost correctly tensioned.
repeat 6 and 7 for all strings.
8, put the locking nut caps back into place loosly
9, tune aproximatly
10, I run my fingers from the bridge to the nut a couple of times to stretch the strings properly. Re-tuning a each time, but only approximately. When the strings stop dropping their tuning by a large amount is the time to stop.
11. Tune the guitar so you’re slightly flat (2 cents on a tuner)
12, lock the nut down.
13, remove the card, the guitar should be aproximatly in tune.
14, use the micro tuners to fine tune the instrument.

I know it sounds long-winded, but after a couple af times it kinda becomes second nature.