A number of my guitars have a Floyd Rose tremolo system with the locking nuts near the headstock.
How can I effectively tune a guitar that has a Floyd Rose locking tremolo?
Loosen the lock screws at the nut. Adjust the fine tuners (on the bridge) to the "middle" position, so you'll have room to fine-tune in either direction.
Ideally, tune one string at a time, with a tuner - trying to get the strings in tune with each other will be tough until everything's almost done, as tightening one string moves the bridge and throws the others out of whack. After several passes over all 6 strings, things should stabilize. Get things as close as possible before locking down, as the fine tuners have limited range.
Lock the screws at the nut, and (again with a tuner) use the fine-tuners to finish the job.
First, unscrew the the locking nuts. Now tune your instrument the usual way. Second, screw again the locking nuts and use the tuning keys located on the Floyd Rose to fine tune.
Never use the standard tuning keys (i.e. the ones that are located on the headstock) while the strings are blocked or you'll get trouble! :)