How To Change Guitar Strings
A Word About String Gauges
Strings come in variety of gauges. The gauge of the string tells you the thickness of the strings. The lower the gauge the thinner the strings, higher gauges mean thicker strings. Most manufactures display the gauge size by the size (diameter) of the high E string (the smallest string). Typical gauges run from .008 to .0012.
Different strings are made for electric guitar and acoustic guitar. The most popular electric guitar gauge is .009. Most acoustic guitar players use .010. Novice and intermediate level guitarists will want to stick with these common gauges.
More experienced guitarists may want to experiment with higher gauges (.011 or .012 and up) because they offer better sustain and tone. Higher gauged strings are harder to play. They feel "heavy" under your fingers and take some getting used to. They'll also make your fingertips quite tender if you're not used to them.
Do not use heavy gauge strings until you have had a guitar technician look at your guitar. Using heavy gauge strings may require adjustments that only a qualified technician should perform.
Changing Guitar Strings
There are thousands of types of guitars and many of them need different methods of changing strings. Use this guide as just an example.
One thing that will help you wind and unwind your strings faster is a little device you'll find at your music shop:

Take you string winder (or if you don't have one, do it by hand) and unwind the top string until it comes off the tuning machine. Trash the old string.

Insert your new string through the bridge or the bottom of the guitar tremelo system:

Pull the string out on the other side:

Insert the string into the tuning machine:

Make sure you line the string up into the nut:

Now take your string winder and wind it up:

Hold the string with your extra hand as below to keep slack out of the string:

Wind the string up until it doesn't rattle against the neck, then clip the access string poking out of the tuning machine:

Repeat this procedure for the other 5 strings.
