On a steel-string guitar, there are usually six little ball-like things that hold the strings in place inside the guitar. You need to remove these string pins.

On a nylon-string guitar, the nylon string is tied to the bridge. At the end of the string, press the string against the corner behind the bridge to form a knot. When you remove the string, just pull the knot apart and you can take it out of the tuning peg hole.

On electric guitars, different brands and models have different ways to remove and string the guitar. Some are held in place by a hard-stop tail, such as Les Paul guitars. Others are inserted through the back of the guitar, such as Strat guitars. For these guitars, you turn the guitar over when you string it. Either way, just push the string in the opposite direction to remove it. If the string is stuck, you can bend the other end back to push it out.

After you remove the old string, put the end of the new string with the ball into the small hole for removing the string. This is easy for steel-string guitars, but for classical guitars, you have to tie a new knot. Specifically, first pass the flexible end through the small hole on the bridge, pull it back through, pass it under the strings, and twist it a few times. Now, pull it in the opposite direction to form a U shape and tie it back. You can also find a tutorial video on YouTube for this part.