Find the musical version of the song. This may be on your computer or a tape or CD. Search for the lyrics as well. A standard search on the Internet should yield the results you are looking for. Just type in the song title followed by lyrics, such as: "Jack and Diane lyrics". Elyrics.net and Metrolyrics.com are two websites that provide song lyrics.
Listen to the song all the way through, singing along what you know. You will probably find that the chorus is the easiest to remember because it is repeated throughout the song. Repetition is one of the most important aspects of memorization.
Look at the lyrics as you sing along and circle your problem areas. This will pinpoint the lyrics of the song that need the most attention. Read through those lyrics carefully. Try to interpret what they mean and how they fit in with the rest of the lyrics and repeat the lyrics aloud. We tend to remember things better when we understand the meaning.
Start from the beginning of the song and write the lyrics down in a notebook without listening to the music. When finished, compare with the original version. Circle or highlight the lyrics you got incorrect.
Work only with the lyrics you wrote down incorrectly, go sentence by sentence and read the correct version of the lyric aloud. Then, cover it up and write it down word for word from memory. Check your work. If you got it correct, move on to the next lyric. If you wrote it down incorrectly again, keep rewriting the lyric until it is correct.
Continue listening to the song whenever you get a chance: in the car, while you workout or in between classes. Repetition and recital are very important in memorizing a song. Practice, practice, practice and soon you will be singing the song by memory without even having to think about it.