Here's how I do it:
1) Level the bridge
2) Adjust neck relief (truss rod adjustment)
3) Adjust saddle height
4) Check and correct intonation (this should be the last thing you do)
What you will notice more than anything is the bridge will pull toward the neck a bit more due to the higher tension of the strings. After you put on the new strings and tune to pitch, tune every string down about a half-step. Very gradually (and in quarter turn increments), screw both trem spring claw screws further into the body until the bridge plate is about level with the body. Hopefully the strings should pretty much be in-tune since you down-tuned before adjusting the bridge.
If you notice right beneath the 24th fret at the base of the neck is a little wheel with holes. Turning this will bow the neck in or out. A heavier gauge of string will cause more bowing in the neck (but not dramatically with the relatively small size increase in string gauge), so using an allen wrench in the wheel's slots to rotate will remove just a slight bit of relief from the neck.
If you have any fret buzz, you will want to very slightly raise the saddles of the affected strings. Conversely, if you want lower action, you will want to slightly lower the saddle heights of the desired strings. This is done by inserting a very skinny allen wrench (I can't remember the exact size off-hand, but the guitar should have come with one) into the tiny holes on either side of the top of the saddles for each string. Each saddle has two screws. Adjust each screw very slightly (up or down, depending on the situation) making sure the saddle is even after both screws have been adjusted. Try out the string to see if the buzzing is gone or if the action is now to your liking. You may end up lowering a string into buzz territory, in which case just raise the saddle slightly.
Intonation is very easy, especially with a non-locking trem. You should do this LAST, as the other adjustments above can all affect the intonation. So if you do intonation first, you'll just have to do it again later. Make sure the guitar is in-tune. Then play a 12th fret touch harmonic. If the 12th fret harmonic is in-tune along with the open string, that string is intonated. If the 12th fret harmonic is not in-tune, but the open string is, you need to make an adjustment. There is a very tiny Phillip's head screw at the rear of the bridge for each string. This screw adjusts intonation. Very slightly adjust the screw until the open string and the 12th fret harmonic are both in tune. Adjusting the screw will throw off the tuning of the open string, so you'll need to keep checking the open string tuning first. This process ensures the notes are the same pitch up and down the string. So, for example, the first fret on the B string is a C. If your B-string is intonated, the first-fret C will have the same correct pitch as the 13th-fret C on the B-string. This process is far more tedious on a double-locking trem like a Floyd Rose.
This is a very basic set-up for any electric guitar (with a non-locking trem) that most shops will charge you $50-$100 to perform.
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