Unless you bought your guitar from a guitar shop and are absolutely certain that they did a "pro set-up", chances are, it needs one.
Terminology you must know before you begin- There are two main parts of a guitar, the body and the neck.
Body- The biggest part of the guitar, where the pick-ups, bridge and pick-guard are attached. The main part, and the heaviest part.
Neck- The long part of the guitar, with the fretboard on the front and the tuning part at the end.
Tuning Keys (or tuners)- The little keys that you turn, to tune the guitar. They are located on the head and one string attaches to each one.
Nut- The little guide-thing that the strings lay in. There is one slot for each string. It is located at the top end of the fretboard and is the divider between the fretboard and the head.
Frets- The little lines on the fretboard. Usually brass, they separate the notes you can play.
Fretboard- The front of the neck, where the frets are and where you press your fingers down on the strings when you play it.
Head (or headstock)- the top part of the guitar, where the tuning keys are located.
Bridge- The part on the body, where the strings attach. Sometimes a tremolo type with a wammy bar.
Pick ups- The little rectangle thing (or things) on the body, that the strings pass over, but don't touch. It picks up the sound and sends a signal to the amplifier.
Pick Guard- A plastic piece that is just below the strings, on the body. It is there to protect the finish from damage caused by your pick slamming up and down on the strings.
What you will need: A small phillips screwdriver, a small flat-head screwdriver, a small pair of wirecutters, a guitar tuner, a cable to plug the guitar into the tuner, a new set of guitar strings (if it's a nice guitar with the action low, you can get away with 09's, but if it's an average guitar, I suggest 10's), some guitar polish and a soft absorbant lint-free cloth (about a square foot is a good size). If you are working with an older guitar with a little rust on some screws, you may want to have some sewing machine oil or 3 in 1 oil handy.
1. Off with the old strings. To begin, the first thing you should do is take off all of the old strings and discard them. Don't cut them off with wirecutters, turn the tuning keys and loosen them enough where you can get them off by hand. Be careful not to give yourself a blood test. (You know how sometimes they will prick your finger for some blood? Well, the ends of the strings will do that to you too, so watch out for those sharp ends of the strings.) Sometimes a little piece of one will be stuck in such a way that you have to use wirecutters to get it out. In this case go ahead, but, be careful not to scratch the guitar and make sure the string is loose enough so that when you cut it, it doesn't snap under pressure and poke your eye out!
2. Make sure everything is tight and working properly. Once all of the strings are off and the bridge and tuning keys are free from string pieces, get your handy little phillips srewdriver and go around to every screw you can find and make sure they are tight. Not too tight, you don't want to strip the wood or crack a piece of plastic, just make sure they are snug.
2a. Notice the bridge- the screws that hold it down should be tight, but the other screws, the ones that adjust string height and length (a.k.a. intonation), should be worked back and forth once each, leaving them in the same position you found them in. (If they are rusty, you may have to put a tiny drop of oil on them to get them to work. Don't oil rusty screws that go into wood, just the ones on the bridge that are there for adjustments.)
2b. Checking tuning keys. If the tuning keys seem to be working properly, just make sure the screws are snug. Jiggle and turn each tuning key to check for tension and play. If one feels tighter or looser than the others, you should take the covers off and inspect them. If you have covered tuners, they may be loose but you can't tell because you can't see them. Remove the two screws on each cover and make sure the screws under there are tight against the wood (get a cup to put the screws in so they don't get lost). If the tuning gears look a little rusty, or feel tight to turn, put a tiny drop of oil on each one, directly on the gear, and work them around, back and forth. The main screw, that goes through the gear, should be snug but not too tight or else it will make tuning difficult. Make sure you wipe off any excess oil (not with your polishing cloth), and put your covers back on.
3. Shine 'er up. Using your guitar polish and dust-free cloth, clean and polish the entire guitar. It's much easier to do this with the strings off, so do it now. Clean the cracks and crevices along the nut, bridge, frets, and tuning keys. Then polish the entire guitar.
4. Put your new strings on. Insert the first string into the bridge and make sure it is seated properly and on the string guide (the top part of the bridge with the slot for the string to lay in). Keeping some tension on the string, so it stays seated on the bridge, lay it toward the tuning keys, being careful not to fold or crease the string.
(Take a look at the tuning keys and determine which way the strings should wrap around them. If your tuners are in-line and all on one side of the headstock, like a Strat, they should all wrap around the same way, which is counter-clockwise on a normal right-handed Strat with the tuners on top. If your in-line tuners are on the bottom, you should wrap them clockwise. If your tuners are split, with three on each side of the head, you should wrap them from the inside of the head. In otherwords, the ones on top should be counter-clockwise and the ones on the bottom should be clockwise. This way, the tension from the strings is aimed at the center of the headstock.)
Holding the string down with your thumb on the fretboard near the nut, to keep it seated on the bridge, insert the string into the little hole on the tuner. Pull the string through until the string has about two inches of pull. (That is to say, you can pick the string up off the neck, no more than two inches.) With one hand holding the string two inches off the neck, and the other hand pulling the string through the hole in the tuners, and knowing which way the string is supposed to wrap around, wrap it the opposite way and pass it under the string, then fold it over the string and pull, keeping two inches of space uner it at the neck. Once you make that pull, it creases the string and holds it from coming out of the tuner. This string wrapping technique (backwards, under, fold over, pull) will help keep your guitar it tune too, especially on the skinny strings.
Now, keeping a little tension on the string, to keep it seated on the bridge, tightnen the tuning key until the two inches of slack is used up. Double check that it is seated properly on the bridge and nut, then tighten it close to tuned.
Using your wirecutters, cut off the excess string sticking out of the tuners. Repeat this process for the rest of the strings. Once you get all of the strings on, grab each string in the center of the neck and stretch it a few times. Then tighten the tuning key a little more, then stretch the string a little more. Be careful not to break the thinner strings as you stretch them, but stretching is important to get it tuned, where it will stay tuned, because new strings will always have to stetch a little before they settle into being able to stay tuned.
5. Tune the guitar. Plug it into a guitar tuner, make sure the volume is turned up on the guitar, then press the button to select E-440, the string on top (also known as the bottom string, because it is the fattest one). Turn the tuning key until the tuner reading is dead-on. Stretch the string a little and tune it better. Stretch it again until it stays in tune after a stretch. Do this for all of the strings. Your guitar is now in tune.
6. Check and adjust the intonation. Notice the 12th fret, with the two dots, instead of one dot? When your string is in tune, put your finger on that note, with the double-dot, and see if it is still in tune. If it is, then the intonation on that string is fine.
Move on to the next string. Again, make sure the string is tuned. Then apply your finger to the double-dot fret and se if it is still reading tuned. If the tuner reading is too low, then you need to adjust the scale-length shorter. In other words, you have to adjust the guide on the bridge, so that it makes the string shorter. If the reading on the tuner indicates that it is tuned too high at the 12th fret, then you need to lengthen the string, or move the bridge-guide back.
When moving these bridge adjustments, you should first loosen the string a little, to relieve the tension off the bridge, then adjust the intonation about an eighth of an inch or less. Then, tune the string again with the guitar tuner and recheck your intonation. Do this until it you get a tuned reading both with an open string, and with your finger on the 12th fret.
7. You're done. Gently put the guitar down and don't bump the tuning keys. Give it to the owner, smile, and say "that'll be seventy bucks." Or, if it is your own guitar, then just pick it up and jam! Then, go buy some picks or something with the money you just saved.