Make sure your instructor selects a song at voice lessons that works with your range. You can't match your voice to a song if your alto voice can't possibly reach the high notes.
Go beyond the notes once you've mastered them. Study the lyrics and try to understand the story that is being told. Say them out loud. Look up words in the dictionary that you might not recognize.
Find out the context of the piece. Is the piece from a play or Broadway musical? For example, knowing the story from "Wicked" will help you sing the character Glinda's perky song "Popular." At voice lessons, ask your instructor to help you research the background of your song.
Connect with the mood of the song by matching your voice to suit the mood. Listen to the piece performed by another musical artist. What emotions do they bring to the song? Do you agree with their choices? Think about what you might contribute to the piece to help interpret the mood.
Bring the music to life by expressing the emotions you find there. Is the song happy or sad? Bluesy or contemporary? Look at the dynamics of the song. Does it call for loud (forte or F) or soft (pianissimo or p)?