There is basically only one thing you will need in order to clean your guitar: a cotton polishing cloth (the same you use to clean your car). In case you have an electric guitar you might also need a screwdriver. Optional things you could use are oil-cutting solvent and polish. You need to test the strings on your guitar first, because it is vital to maintain good pitch and tone on your guitar.
In case your strings are not good anymore you should buy new strings and replace them (with a speed winder). Speed wind the strings (one by one) until they are loose enough to pull off the guitar. In order to remove them, unwind them from the neck. Do NOT cut them, or these problems may occur: When you try to get the cutters around the string you can damage the wood or leave permanent marks, it could cause the bridge-tension to recoil and bounce out of place because it is a sudden tension-release & when you have extremely taught strings, they can fly all over the place (including your eyes).
You should examine the pickups in case you have an electric guitar. Unscrew the faceplate in case they look rusty. While removing the pickups, do not disturb the wiring inside the guitar. You may use any common rust dissolving agent to clean the rust, when you are done, put the pickups back in place and polish them.
The next thing to do is checking the fretboard. Sweat and oil from your hands sullies the wood and dull the sound after weeks of play. Take a look at the nut as well, take out the string and lubricate the groove with soap or a professional solution. Dry and replace the string, this will keep it in tune.
Clean the fretboard with a damp cloth. This method works great on all types of finishes. In case there is a lot of grease on the body, you can also use a gentle oil-cutting solvent. Clean the body of your guitar because grease and oil from your hands will build up there over time. On clear, shiny finishes you may also use polish (make sure it is recommended for guitars). Make sure you do NOT use polish on a satin finish (not shiny). After polishing your guitar use a damp cloth to wipe off the bridge. In order to remove embedded dirt you can use a small toothbrush if it needs more than a perfunctory cleaning.