you should check out the
circle of fifths
it tells you which minor has the same note like major. i cant really explain well. just google it or look here on tb. just a short version
maj notes = minor notes
C/Am
G/Em | has 1# which is f#
D/Bm | has 2# which are f# c#
A/F#m |... 3# f# c# g#
E/C#m | ...4# f# c# g# d#
B/G#m | ...5# f# c# g# d# a#
F#/D#m| ...6# f# c# g# d# a# e# (e# would be F obviously.. enharmonic)
F/Dm | has 1b which is Bb
Bb/Gm | has 2b which are Bb Eb
Eb/Cm | ...3b Bb Eb Ab
Ab/Fm | ...4b Bb Eb Ab Db
Db/Bb | ...5b Bb Eb Ab Db Gb
Gb/Eb | ...6b Bb Eb Ab Db Gb Fb (which would be E obviously..)
So that means when the chord that is played is eg Bb you can check the circle of fifths (whilch after a while should be in you brain

) and know you could play a Gm over it. because those have the same note in it. which are C,D,Eb,F,G,A,Bb.
hope you could understand that and that it helps. but best thing to do is to check out the net.
for example here's a graphic. but there are better ones..
http://library.thinkquest.org/05aug/..._of_fifths.gif