The double locking nut feature of Authentic Floyd Rose tremolo systems ensures tuning stability that's unmatched. Achieving that stability can have a few unintended challenges such as changing strings. We have outlined a step by step process.
Unlock the three clamps at the nut with the 3mm allen wrench provided with the guitar or bridge.
Set the fine-tuners on the bridge to the middle of their tuning range.
Change one string at a time (starting at either E string) by first loosening the string and unclamping it at the saddle with the 3mm allen wrench.
Cut the ball end off the replacement string with a pair of wire cutters.
Place the freshly cut string end into the center of the saddle and tighten the clamping screw until it is difficult to turn.
Thread the other end of the string under its nut clamp and under the string hold down bar, then to the tuning key and tune the string. [Pull on the string until it is tight around the tuning key and retune.]
Repeat 2 through 5 until all strings are replaced.
Check your tuning on all strings once again.
Re-clamp the three nut clamps.
Check your tuning once again making any adjustments this time with your fine-tuners only.