The easiest way to recognize modulation would not be to listen for a pivot (this would be better if you have a score to look at), as pivots are frequently diatonic chords in both the former and the new key.
Instead, listen for the new dominant. Frequently the composer will use a dominant 7th chord, which has a very distinct sound that you should be able to easily pick up on. Following the dominant chord will be the new tonic.
Now that you know which chord is the tonic, just try to listen for which pitch of the chord is the root, and compare it to the root of the old tonic.
If old key was major, common new keys would be IV, V, iii, vi.
If old key was minor, common new keys would be iv, V, III, VI.