My technique is to first remove all the strings, then start with the low E string, then the high E string and work your way toward the center. It's debatable as to whether it even matters what order you put the strings on, but it's not a bad idea to find a routine and stick to that.

So, starting with the low E, first I pull the string through the tuning peg, then put my fist under the string in the middle of the neck. This just gives you kind of an idea of how much of the string should be wrapped around the tuning peg and how much you can snip off. Add about half an inch of slack to that estimation, just to make sure you have enough string to keep it tight around the peg. Some people snip the excess string at this point, but I think it's better to leave it for now so you know you'll have enough slack. It sucks when your strings pop off because there's not enough string wound around the tuning peg.

As I'm adding strings, I tighten each one roughly to its intended note (if you can do that by ear; if not, just guess).

Once all the strings are on they need to be stretched out. Stretch them every which way: pull on them up and down the length of the neck, bend them up and down, yank them, snap them, and just generally give them a good workout. Then use whatever tuning device you have to put it in tune. You'll probably have to repeat this three or four times to get the strings to stretch out enough so that they stay in tune.

Finally, If there's one thing that makes string-changing immensely less frustrating, it would have to be a string winder (e.g. http://store.musicbasics.com/gace-winder.html). They're cheap and will save you hours of frustration.

N.B.: This is just my personal technique; each player has his/her own set of rituals and tricks, and there are plenty of videos on the web that show the basics.