When a piece of music is said to be in a certain "key", it means that the melody (and chords) consist predominantly of notes within the corresponding scale. Thus a piece of music in the key of C will predominantly contain C, D, E, F, G, A and B notes (i.e., the same notes which occur in the C major scale).
Occasionally notes "outside" of the scale occur, but their appearance will not be common. Thus in the key of C you should not expect to see too many sharps or flats.
The following songs are both in the key of C, featuring notes taken from the C major scale.
The term andante means to play at a slow, easy walking pace. Follow the count for the lead-in notes carefully and observe the tie in bar 2.