In my experience, it's easiest to do the following:
1) Unlock the locking nut
2) Set all the fine tuners to a position where you have equal play in both directions
3) Tune the guitar with the machine heads, HOWEVER, do NOT tune it EADGBE, but instead use the following:
E - about 75 cents sharp
A - about 50 cents sharp
D - about 25 cents sharp
G - about 10-15 cents sharp
B - tune to B
E - tune to E
4) Lock the locking nut and then use the fine tuners to make small adjustments.
I've found this method, especially with my 7 string guitar saves me a lot of fine tuning (I set the low B string around a 100cent sharp) as once you lock the nut, everything is roughly at EADGBE so you don't have to keep faffing about trying to get the low strings in tune. You don't have to be super accurate with step 3, and it's easier to adjust than using the fine tuners anyway. If it makes it even easier, think of the bridge as a line balanced on a point. I prefer tuning in this order: E (low), E (high), A, B, D, G so you work from the outside in so as not to 'tip the scales', although it is always the lowest strings which get 'off balance' the easiest. With the machine heads you can usually tune E to E without too much of a problem though, then clamp it down and make the small changes with the fine tuners.
Floating bridges are a PITA though, but it's the price you pay for wanting to abuse a whammy bar.
Edited by Somnambulist - 8/17/11 at 11:58am