This is funny.. it's a question that initially makes people go huh?? did he just ask that?? but there isn't a ton of info on it and I know a lot of grown adults that take their guitars in to be changed.. baffles me but maybe it's because they have LPs and they get tired of the bridge falling off!!
Here's what i've done and I never have unwinding..
1. put the string through the bridge and run it through the post. I have the post positioned so the string goes through on the right hand side and bends back through towards the bridge again (6 inline right handed)
2. My trick for getting the windings right is I hold the string down on the fretboard with my index finger, then with my other fingers I pull the string up high, about 3-4 inches off the fretboard. This does 2 things.. 1 it puts tension on the string for winding, and 2 it makes sure you have enough string to get several good winds around the post.
3. I wind with a 2 dollar crank string winder. Or if i misplaced it I do it the hard way.
4. The post. Make sure after the first wind that the string runs under each wind before it so as it goes it's being forced down toward the peghead. You want a downward angle on the string anyway.. Letting it crawl up the post is asking for trouble if you dont' have string trees.
5. I get 5-6 good winds on each string, less on the bass string and probably more, 6-8 on the high E.
Tips.. change 1 string at a time, starting with bass. After it's tuned to pitch, gently pull on the string, tune it to pitch.. repeat until pulling no longer gets it out of tune. If you have a trem, you could yank back on the trem instead of pulling the string..
Now.. if you're using a locking trem.. Change 1 string at a time still.. Tune to pitch.. You may have to torque down the springs in the back somewhat if you're going heavier string gauge.. but you don't have to work so hard at the stretching part. Just lock down the nut clamps (that sounded painful) and there shouldn't be any stretching to speak of.. If there is the fine tuners should work just fine. Dont forget to center out the fine tuners too before you start of you may find yourself at the end of their travel and have to restring again.
Hope that helps some.. who knows, maybe some others wondered and were afraid to ask..
-m