Turn the tuning knobs located on the head of the guitar in the direction that loosens the strings. You'll be able to tell if the string is getting loose because the note will become lower when you pluck the string. Turn the tuning knob in the opposite direction if the note you plucked becomes higher. Loosen all six strings until they become very slack.
Pull the strings--starting with the low E string--out of the tuning peg hole through which it's been strung on the head of the guitar. Push them out through their respective back holes located on the back side of the body of the guitar.
Open your new pack of strings, and look at the name and size of each string, indicated on the paper sleeves in which they are packaged. It doesn't matter which string you start with, but I typically put my low E string in, then my high e string, then my A string, then my B string, and finally my D string, followed by my G string.
Begin putting the low E string in by placing the end which doesn't have a metal ball on it through the proper hole on the back of the body of the guitar. Make sure it's going through the right hole, once you place it through, as the holes on the back of the guitar are opposite of those on the front.
Pull the string so that it's tight and the ball on the other end is all the way in the hole on the back of the guitar. With the end of the string that's been laced through the hole, pull it up to the head of the guitar, and align with its respective crevice in the nut (the thin white horizontal bar that's in between the head of the guitar and the first fret).
Wrap it around the proper tuning peg a couple of times, and then lace the end through the hole. Pull it as tightly as you can, and then begin tightening the tuning knob. Repeat steps four through six with the five remaining strings. Tune the strings with a tuner a few times in a row. Because they're brand new, they'll most likely come out of tune almost instantly.
Cut the excess string off with a wire cutter, but only after a week or so. Cutting it too soon will make the strings come out of tune more often.