String Winding Techniques

	.	Step one is relatively simple. After securing the string down at the bridge, pass the loose end through the eyelet on the tuning post. The free end of the string is indicated in these images by the little red ball (not too imaginative, but it was the best I could do).
		Next, either by turning the tuning peg or by wrapping the string up and over the post, start to wind the string onto the post. Personally, I prefer to use the tuning pegs for this task; the string almost ALWAYS winds on neater, and it seems to twist the string less. Make sure the first loop of your winding passes OVER the free end of the string.
		On the next winding, make sure the loop winds UNDER the free end of the string. I feel like this helps to "lock" the string in place and discourage slipping.
		Keep winding the string on (at this point, you're probably gonna HAVE to do it with the tuning pegs rather than simply wrapping), making sure that the loops pass UNDER the free end of the string.

Other Thoughts

You will require fewer windings on the thicker guitar strings than on the plain strings (you can get by on as few as two or three). The low E, A, and D strings in particular seem to kink onto the tuning peg pretty easily, and this kinking resists slippage. The plain strings (the high E, B, and - depending on your gauge - G strings) will probably need at least 4-6 windings to really lock in place.

You should try to keep as little string as possible on the tuning pegs; lots of excess string means extra string length that can slip and stretch, causing tuning problems.

To cut down on string slippage later, I always make string stretching a part of my string-change process. I always give them a sound tug, just to make sure they're stretched well (see above illustration).

Then, once each of the strings has been tugged at, and the guitar has been re-tuned, I perform a series of radical bends on each of the strings, both low and high on the neck. On your FIRST pass at bending, I'll bet you notice a change in the pitches. Tune up and do it again. After a couple of times, the strings will be pretty well settled, and should be relatively stable for the remainder of their use.

This may sound like a lot of trouble, but the whole process takes me no more than a minute or two longer than other string-changing approaches, and I find that the tuning stability it offers is well worth the extra minutes.