You want to make your performance well rounded and interesting to the audience, so you need to do some detective work on your song. Take a close look into the character singing the song. Every song has a character and a story to tell. Sometimes the character is just like you and sometimes it’s someone very different.
Getting into character means temporarily inhabiting the life and circumstances of a character for a story. In this case, the story is presented in the lyrics of the song. If the lyrics are from an opera or musical, your song and your character have an entire life for you to explore. Songs from the radio usually aren’t from a show, so you get to decide the circumstances.
If you just can’t find the answers to some of the questions about the character singing the song, make a good guess based on the other details you’ve read in the script, or create a story or scenario that supports the words of the song.
Making up the missing details of your character’s life helps you create a complete picture of exactly who this person is. As long as your scenario leads you to say and sing the words on the page, it can work. If your scenario is so far fetched that it distracts you and you’re too busy to sing, make it a little less complicated for now. Simple is good.