In case you've resided in a 300w mega-stack-proof bunker for the last 30 years you will find that of the various tremolo systems out there, the Floyd Rose tremolo is by far the best. This is because of many essential construction points and revolutionary design breakthroughs:
1. The bridge plate itself is made out of hardened steel, this is important because the FR pivots on two pivot posts in the guitar which ensure that the bridge returns to "zero" (a balanced point at which tuning is standard and the bridge is resting at the same angle as the body).
2. The FR is a double locking system which means that the strings are locked at the saddle as well as the nut this eliminates the usual tuning issues which are often experienced with plastic nuts that bind the string or poorly grooved saddles.
3. The FR is quite a simple design which means less things can go wrong which is always a good thing.
Now there are many companies that use fake or "licensed" FR bridges which in the beginning work but the knife edges (the part of the bridge plate that rests against the studs) will soon wear out, This causes numerous setup and tuning issues. On Whiskers, luthier Simon Pinder installed a original German Floyd Rose. These are expensive ($170 US) but definitely worth it in the long run.
An excellent site for info on tremolos in general is Audio Zone DK (tremolo page) , that site has a section which covers everything from cleaning to repairing tremolo bridges.
Anyway getting back to the point, here are a couple of picture provided by Simon Pinder of the installation process (I messed up the positioning of the mounting stud holes).
Here you can see the shim he created for mounting the locking nut:
Simon Pinder filling my poorly positioned mounting stud holes, A quick tip: what Mr. Pinder does is collect broken drum sticks which can then be used as dowels.
Here we can see the studs finally positioned properly, It is important that these studs go into the guitar body perfectly straight, I suggest using a drill press or a jig for a hand-held drill.
Here is a final picture of the floyd rose installed with an EVH D-tuna: