Learn to recognise the key that any given piece of music begins in. This starting key is called the tonic key, and can be found easily by looking at the key signature, and checking for the possible raised seventh note (leading note) which shows if the key is minor. This may require you to learn the "three semitones down" rule for finding the relative minor key, or the circle of 5ths. If you play an instrument you will find that you can learn key signatures pretty quickly by practicing recognition on each piece of music that you play.
Also learn to recognise if the piece has modulated into a different key - this can be seen by accidentals that make the notes of a different scale. Be careful here that the piece isn't simply chromatic, or that it hasn't become modal.
Learn to recognise when a piece of music becomes modal - 'sounds like medieval or church music' is probably the best description. There are different modes, although it's not necessary to be able to name the mode that the segment is in (it might help with points though)