You must know the level of difficulty of this task and make yourself ready to put an honest effort. If you are new to the Italian language, there will be a phase when you will think to leave but keep practicing as this is the only way.
Know the music:
You must know the music and the feel of that song. Try to play it over again on some music instrument. If you do not play any music instrument then get a karaoke machine to record and play the music easily. Trust me, knowing the melody really helps you in memorizing the lyrics of a song.
Pick your song:
If your proficiency in Italian is not great then pick a song which is not lengthy. Moreover, you should select a song whose lyrics are understandable and easy. You can buy an album from the market or just browse the internet to pick a reasonable song. You can also get a sheet of lyrics from different music sharing websites.
Write on the flash cards:
If you are finding it difficult then use flash cards to memorize the lyrics. Write four or five lines on each flash card, play the song over again to understand the lyrics. Keep doing this exercise until you are confident enough to sing along with the original track.
Listen to the song before going to sleep:
Recent studies show that the things you do before sleeping stick to your mind. Use this technique to memorize your favourite Italian song. Just listen to that song or at least read the lyrics before going to bed.
Sing in front of people:
Singing in front of various people every time can really help you in memorizing the lyrics as your concentration level is always high while performing in front of the audience.