What kind of tremolo is it?
Either way your first take an allen wrench and loosen the screws on the nut. Then loosen one string. If its a Floyd Rose, there is another allen screw at the butt of the bridge. Loosen that and you can pull the string out of the bridge. If its a Kahler, then it may slide out of the bridge lika a normal guitar.
Restring 1 string at a time. On a Floyd Rose, you will need to cut the ball off the end of the string, and feed it back into the "pinch point" of the bridge where you took the old one out. Tighten the screw at the end back up and move on to the next one.
DO NOT tighten the nut on top until you do the following:
AFTER all the strings have been replaced, tune the guitar and then take each string and stretch it up and down by pulling it. Tune up again and repeat this process like 2 more times. Your strings will stretch more than you think and this will help you stay in tune.
Next check your fine tuners on the bridge and make sure none of them are screwed all the way down (or up for that matter) I generally unscrew them 3/4 of the way out since strings stretch, and they get screwed in to get back in tune (tension increases)
Once you are confident you have stretched them good, tune it up and tighten down the nut. You may need small adjustments with the fine tuners, but you should be good to go.
And don't forget Whammy rule #1
Every time you push it down, youll have to pull it up to stay in tune decently.
Kinda like Newtons law.
OR you can pull it up just before you do a dive bomb and the effect would be the same.
Hope that helps!