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. Here is an example.
A dot written after a quarter note means that you hold the note for one and a half beats.
A dotted quarter note is often followed by an eighth note.