Restringing your guitar

Whether nylon or steel, strings come in many gauges, or thicknesses. Nylon strings are scarcer than steel, and there are usually only a couple of different gauges to choose from. Heavier strings have greater volume, but are harder on the fingers. Even nylon strings appear to be metallic as the thicker strings use fine wire wrapping to beef them up. You'll find there are cheap sets, and expensive sets. Unless you're performing a concert tomorrow night, the cheaper are fine.

Steel strings come in a huge variety of gauges; they can be round wound or flat wound. The flat wound use a ribbon of metal to wrap the thicker strings rather than plain wire. All brands sell strings in sets of 6, and it's recommended that you change them all at the same time so that your guitar sounds even.

Strings wear out and break. Body chemistry has a lot to do wirth how often you need to change them, but rule of thumb is, when they sound dull and become hard to tune up, it's time.
Nylon strings

Nylon strings must be tied to the bridge in such a way as to not slip under tension . The illustrations below indicate the proper way to do this. The thicker bass strings often have one end which is floppier and more bendable than the other. This is the end to use at the bridge. Make sure the twisting continues over the back edge of the bridge. This ensures that as the string is tuned up and the tension increases, the friction becomes greater and the string is well and truly fixed.
Steel strings

Steel strings are much easier to put on. All have a "ball end" which stops the string at one end.

Most acoustic guitars have a bridge with pegs that are inserted into the holes that accept the ball end of the string. Push the ball end into the holes so that the ball drops inside the guitar, then push the peg back in the hole and gently pull the string until you feel the ball is being stopped by the peg. When you feel this contact, really push the peg hard into its hole. As you tune up, you may have to keep your finger on the peg and apply pressure to keep it popping back out.

Electric guitars can be strung in a variety of ways, all of them obvious: one way or another, the ball end keeps the string from slipping through whatever device is fitted at the bridge or tailpiece..

There are also a variety of tuning gears, where the other end goes. Again, most are obvious. If it's the simple "push it through a hole in the peg", try pushing it through twice if you can.

You should leave enough slack so that it winds itself around the peg a few times before it comes up to full tension. Once you've tuned up, use a pair of pliers to snip the excess length off, or you'll be hearing all kinds of buzzing and vibrating going on.