Frank,
This is for basses:
I usually insert the ball into the tailpiece, bring the string up to it's tuning post, curl over the top and go past ~ the width of my hand. I cut the string using a heavy wire cutter (only on the silk wrap portion). Keeping the string pulled tight, I insert the cut end into the center of the tuning post, bend down at the slot of the post and wrap at least the first turn around the post by hand. The rest easily wraps up by the tuning key. I always get 3 wraps on the peg using this method, and you can easily unhook the ball to untwist the string once the first wrap is on the post. My advise is to make sure the string you use is a match to the scale length of your guitar, or else you might end up with wrap in the nut or speaking length on the peg, both undesireables. Some strings do not have a silk wrap (DR is one) and I just make sure I do not cut too far into the string. I have not had a problem with the cut end captured inside the center of the tuning peg. It won't unravel since I also put a 90 deg bend in the string as it comes out of the tuning peg slot. Eugene's method of cutting the string after it is at pitch requires you to allow the uncut extra to dangle out of the tuner and cut it as close to the side as you can get. This leaves a rough cut end that can grab onto things and scratch clothes, etc. IMO it looks less clean.
Kris