The F minor melodic scale is made up of the notes F, G, A flat, B flat, C, D, E, and back to the F on the upward motion of the scale. Coming back down the notes change slightly to E flat, D flat, C, B flat, A flat, G, and finally F.
For the right hand fingering, the thumb starts on the F. Work your way up until the fourth finger hits the B flat. Now cross your thumb under and continue up the scale. You will end with your fourth finger on the F. Reverse the procedure to come back down the scale. Remember to change the first two notes that you hit on the way back down.
The left hand starts off with the pinky on the F. Work your way up finger by finger until your thumb hits the C. Next bring your third finger over to the D and continue until you finish the scale with your thumb on the F. Coming back down the scale is just the opposite.
For the next lesson, check out the F Sharp Minor Harmonic Scale.