1) Use something like a block of wood, a wine cork, or a wallet to hold the bridge in place at the angle you want it to be when you’re finished. The goal is to temporarily make your guitar a fixed-bridge so you can…
2) …re-string it like it was fixed-bridge guitar. As you go, be sure to REALLY stretch out the strings. When you’re finished, the strings should be in tune with the bridge plate sitting level with the guitar body. If you’re working on an Ibanez Edge, remember that it’s wedge-shaped. You want the BOTTOM PLATE level, not the face of the bridge.
3) Lock the strings down and re-tune using the fine tuners if necessary.
4) Remove whatever you used to hold the bridge level. The bridge will immediately go out of adjustment and wreck the tuning*. Don’t panic. And more importantly, DO NOT TRY TO TUNE THE GUITAR WITH THE TUNERS OR FINE TUNERS. Remember, it was in tune a minute ago when the bridge was level, right?
5) Adjust the spring tension in the back of the guitar (should be two big screws) until the bridge is sitting at the correct angle again. The strings should now be more or less in tune. Continue adjusting the springs to finish getting them in tune.
Now your guitar is set up with the strings in tune and the bridge sitting at the proper angle, and you didn’t have to spend hours chasing the bridge as the strings went sharp and flat.
* NOTE: If you’re using the same gauge strings and did a good job stretching the new set, the bridge may do very little settling. Give the bar a few shakes. If everything stays in tune, call it a job well done.