Simply pull the springs. Leave the nut locked, and when you put the springs back on you'll be surprised at how close the thing is to tune.
Get yourself a spring puller (the ones made for automotive and motorcycle applications work just as well as the ones that Stew-Mac sells) or a right-angle chisel pick and come in underneath the spring seat into the trem block, and gently pull up. Be careful to do this gently, otherwise you run the risk of sending a spring end into the finish on the back of the guitar.
You can also use needle-nose pliers too, but I think that's probably more of a risk to finish damage.
Set your action, then put the trem back on the posts and re-add the springs. Measure, and lather-rinse-repeat if you didn't get it right the first time.
Rich's tech page on floating trems @ ibanezrules details this pretty well.
For actually putting strings back on where you have spring tension against the block and no strings on the guitar at all, you can perform some variation on using the bar to add some form of tension.
The way I do it on an Original Edge or OFR (kinda hack-ish, but it gets things done) is to trim the string to length (generally I go from the tuning peg, through the nut, to the back of the trem route) and then install the bar. While holding the bar down, I unlock the saddle, and then release the bar (sending the back of the trem against the route). I'll then insert the string into the saddle (against the saddle block) and then hold the bar down to then tighten the saddle lock. Lather, rinse, repeat for the bass (wound) strings.
Once you have all three bass strings on, you should be able to wind 'em up to provide enough tension that you don't need the bar to keep the back of the trem out of the route, so you should be able to add the treble strings without issue. Then, I stretch the strings out and then approximate a tune, and check where I'm at from a trem angle perspective. Adjust trem angle with the cavity claw screws and approximate tuning to get things right, and quickly check intonation.
If it's all fine, then go play.
Hope that helped some.