Songs in minor keys usually have notes that don't "belong" in the key, strictly speaking. For example, A minor is the relative minor of C maj.:

A B C D E F G A

One can call this "A Aeolian", if one is feeling modal.

The chord on the fifth degree of Am would be Em7: E G B D
However, people often want E7 -> Am rather than Em7 --> Am. V7 ("V" meaning a chord on the fifth degree of the scale and with a major third) resolving to the tonic (a chord on the first degree of the scale, that is, the main chord for the key we're in) is what people seem to want. So, Em7 is often replaced with E7 when playing in Am. What does this mean? The only note that's changed is G --> G#. But G# is the leading tone of A, i.e., people seem to think that a G# "leads" to an A more than a G does. This isn't a coincidence. If we break down a simple progression from E7 --> Am it could look like this:

E --> E (It stays where it is)
G# --> A
B --> A or C
D --> E or C

This is really the secret of harmony (or maybe _a_ secret): voice leading, i.e., one thinks of each of the notes being played as a voice and moving from note to note. When people are thinking about writing harmonies, they are often striving for "smooth" voice leading.   

There are three common minor scales: the natural minor, the melodic minor and the harmonic minor. Many songs in minor keys will use both the major and minor sixth and the major and minor seventh, depending on whether the melody is ascending or descending. That is, one might use the major seventh when ascending so as to use the leading tone, but the minor seventh when descending. When ascending, one might use the major sixth in order to avoid the large gap between the minor sixth and the major seventh, but the minor sixth when descending, because one is playing the minor seventh, so there isn't a large gap between the sixth and the seventh.

The Dorian mode is fairly popular. It has the minor third, the major sixth and the minor seventh.

There's nothing magic about any of these scales; what really counts is the melody. One could invent any number of scales with various combinations of intervals. What I find really helps is to learn the sounds of the various intervals (and chords).

From my point of view, the real use of practicing this sort of thing is to train one's musical intuition.