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"). 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. The following song contains three lead-in notes. The melody contains both ties and eighth rests. Listen carefully while watching the music. This will help you get a feel for the rhythms and the pitches of the notes.