Hi guys. I'm having problems tuning my Ibanez, which has a Floyd Rose. I just put new strings on it, followed the instructions in the Alfred's maintenance manual I have, but I can't properly tune the strings. I've tried going from 6th to 1st, and 1st to 6th string, but every time I tune one string, the last one I tuned goes flat. I noticed that the bridge rises every time I tighten one string. Is there something I should be doing to keep it in place, or is something worn out internally? It's a pretty old second hand guitar.
Nope, that's how tuning a floating bridge works...
Tuning and adjusting a floating bridge is a balancing act; The tension of the strings is fighting the tensions of the springs (in the back), hopefully leveling your bridge.

Read the thread linked in my signature, it has a really in-depth guide on how to tune and set-up the bridge. It will also tell you what a bridge looks like after it's been properly set up.
It takes time but once you get it set and leveled out it will come into tune try alternating strings 6th then 1st then 5th and then 2nd then 4th and 3rd strings it might come into tune faster.

That's what I always reference. It's easiest to get it close then tune you deeper strings higher than they should be, gradually changing how much higher as you work toward the high E string. When you get the high E tuned perfect the other string should have lost tension and be closer to where you want them.
Thanks for the help guys, I'll try again when I'm off work.