There are many different ways to change your guitar strings. It is important to change them the proper way, or your guitar will keep going out of tune. Many people do not know the right way to change them, and in result their guitar will rapidly go out of tune and have a hard time keeping the right tension on the strings. What happens is as you strum, pick, bend strings, if they aren't installed correctly will move around it will sound awful and can drive you crazy.
After 20 years of experience, here is what I do. First of all, do one string at a time, I start with the low E string, the top string on the guitar. Cut it in the middle then remove the string. Next, depending on if it is an electric or acoustic guitar, get the string through the bridge. Once it is in there, pull the string tight towards the tuning peg, without putting the string through the whole yet, wrap the string around 1-2 times, then put the string through the whole, above the 1-2 wraps you made. What this method does is make it so you don't have to wind the string a million times to wrap it around the tuning peg. We are first wrapping it, then putting in the whole, and then tightening the tension on the string. Once you have it in there nice, tune the string using a tuner.
Continue this method for all the rest of the strings. As the strings get thinner, you can do more wraps before putting through the tuning peg whole, so on the D and G strings do 3-4 wraps and on the B and E strings do 4-5. It is also hard to do the thinner strings because your wraps want to overlap. Do not let them overlap, it will create tuning issues. To prevent this make sure to pull the string tight and keep lots of tension on it so your wraps are nice and tight and don't overlap.
Once all the strings are on and in tune, now you want to stretch the strings. We do this to take out any slack and get the string tight so it won't go out of tune. To stretch the string simply pull up and down on the string up and down from the nut to the bridge. It will go very out of tune. Retune it and repeat this process for each one.
Once you completed stretching every one a few times and retuning, then you want to tune all your strings up a half step and put the guitar away for overnight.
Come back the next day and see if it is in tune, it should be pretty close. Now stretch the strings one more time, retune, and you should have a nice fresh set of strings on your guitar that won't go out of tune!
