If you are anything like me, you would rather spend your time playing your guitar than tuning it. And when it comes to tuning a guitar with a floating tremolo bridge, such as a Floyd Rose, it can be a long and tedious process, especially when installing new strings. But there actually is an easier way to do it that I did not figure out right away. Here's how to do it:
Insert the tremolo spring cover or a credit card or something else rigid and thin enough to slide between the guitar body and the bottom of the posts that clamp the strings in place. You want to get it so the base plate of the bridge is parallel to the guitar body. Playing cards work well to shim it to the proper angle. You may want to place a piece of cloth between the cover and your guitar's finish to prevent indentation or scratching first. If your guitar does not have a gap between the bottom of the tremolo and top of body, flip it over and you can wedge something between the tremolo sustain block (the thing on the bottom of the bridge that the springs are attached to) and the body. The idea here is to prevent the bridge from pivoting upward (as if you were pulling up on the tremolo arm).
Next, tighten the springs so that the bridge still clamps down on the shims and body even with one string removed. This will allow you to tune, lock the nut, and then fine tune all of the strings without worrying about the spring tension or the other strings falling out of tune as you work.
Tune each string to pitch. If the tremolo starts to pull away from the shims, simply tighten the tremolo springs until the base plate is parallel to the body again.
Once all the strings are tuned, slowly decrease the spring tension by backing out the screws on the tremolo claw until the shims that you put underneath the bridge slide out.