I think the part that's kinda difficult for me to explain is the tuning up part. I have a quick way of initially tuning up the fresh strings mid way starting with the Low E onto the A then the D, G, B and lastly the High E and then back to the Low E again and the same way to the high E until I reach the standard pitch. Then I'll start strectching the strings starting with the low E and then tuning back up. I'll strech it again for up to 3 times and tune up before I go the A String and then the rest. I'll then start the fine tuning from the D string followed by A and Low E. Then I'll fine tune the plain strings starting with the G followed by B and lastly High E.
Heh, reading the above also makes my eyes go kinda screwy but it's pretty much how I've managed all my own floating bridge guitars. My Strat too.