Sometimes a song does not begin on the first beat of a bar. Any notes which come before the first full bar are called lead-in notes (or "pick-up notes", or an "anacrusis"). When lead-in notes are used, the last bar is also incomplete. The notes in the lead-in and the notes in the last bar add up to one full bar.
Exercise 55, Greensleeves contains one lead-in note. When lead-in notes are used, it means that the melody begins before the accompaniment. This means you will probably need a reference pitch for your starting note in order to be sure you are singing the correct pitch.
Before you begin the song, get somebody to play first the note or chord of the key, and then the starting note on an instrument. Hum the starting note to yourself for a few seconds until you are confident of the note and then begin counting the song in.
You can try this on the following example, which demonstrates a lead-in for the song Greensleeves. The chord is an E minor chord because the song has been recorded in the key of E minor and the lead-in note is also an E note.