Restringing my Ibanez Artcore guitar?

I have an Ibanez Artcore AG75, and when I was restringing it, I
realized (I'm no expert) that the bridge is not actually attached to
the guitar, but rather held down by the tension of the strings. What
is the best way to restring it to maintain the tuning? I realize that
if the bridge is not put in the proper place, the string length from
bridge-to-nut will be different, so the frets won't necessarily match
up and it will sound very out of tune.