Learning to restring a guitar is a lot easier than you might first think, if you do it the right way. If you can't do it at the moment, and are taking it to your local store to get it done, now is the time to learn.
Do be careful though, there is a lot of tension on guitar strings, and if they come loose or snap, they can do you some damage (especially your eyes).
Also be careful to dispose of your old string carefully. Cats and dogs really like to chew on them, but they can go straight through their cheeks. So please dispose of them safely (perhaps rolled up and wrapped in paper?).
Step 1 - Remove and replace
Steel string acoustic guitars have a quite different way of attaching the strings at the bridge end. They rely on a plastic pin to secure the string in place. Again the first step is to remove all of the original string. Just pull off any remnants from the tuning peg (I usually use long nose pliers so I don't poke the string into my fingers).
The ball on most steel string acoustics will just fall into the body of the guitar, and can be removed by shaking the guitar about until it falls out the soundhole (can sometimes prove quite difficult, but is not that important if the ball rattles around inside). You might also like to watch my stupid video about getting a pick out of an acoustic guitar ;)
Next remove the appropriate peg from the bridge. Then put the ball end of the string 10 cm into the hole and replace the peg. Then slowly pull the string while keeping some pressure on the peg until the string is tight. Although this may look a little insecure, if done correctly it will be very strong. Watch out if the peg seems to be coming out, just keep pushing it in (quite hard). Once pulled tight it should not have any give.
Step 2 - Winding on the peg
This part is the same for all types of guitars (except classical guitars). The most important part of this is getting the string on the right side of the peg, and here is how to do it. First of all line up the hole in the peg so it is facing straight down the neck. Put the string through the hole and pull it back so you have some slack. The amount of slack you need will vary, depending on the thickness of the string. The 6th string only needs about 7cm but the 1st string can take 10cm, or thereabouts. Now hold the string in place with your right hand, just hold the peg so the string cannot slip and then turn the peg ANTI-CLOCKWISE if you are looking at the peg (if the peg is underneath like on some Gibson guitars then it looks clockwise from above).
As you continue turning the peg the string will wrap around it. The first time round the string should go above the hole (and the slack poking out) and above the string and after 1 lap it should go under the string. This will make it lock onto the string as it gets tighter (it is OK for all the wraps to go under, it is just more secure if you get the lock). You should aim for a least 3 wraps on the 6th string and 5 wraps for the 1st string. More will not hurt, but less and the string may start to slip. Try not let the string overlap itself, as this may make it easier to break.
Step 3- Tuning up
The next step is to tune the string. I strongly recommend getting an electric tuner, as it is important to hear what the guitar should sound like when you are learning, and electric tuners are pretty cheap these days (I recommend the Boss TU-12 Tuner. I have had mine for 10 years, it gets a beating, but is still working fine). If you have one then tune up using this, if not, tune to another string that you know is in tune. If this is not an option, then tune up to a keyboard, pitch pipes, or whatever is available. See the lesson on tuning in The Basics.
Step 4- Stretching in
And lastly, and quite often forgotten, is to stretch the string in. Just gently pull on the string with your right hand, using your left hand to hold the string in its correct position in the nut. You should notice it going out of tune considerably, and will need to tune it again. Continue stretching until you no longer need to tune it up.
Video Part 1
Video Part 2