The F sharp minor melodic, like all melodic scales, has two notes change on the way down from what they were on the way up. The notes of the scale going up are F#, G#, A, B, C#, D#, E# and back to F#. Coming down the E# and the D# change to E natural and D natural.
To finger the scale in the right hand, start with the second finger on the F#. Work your way to the third finger, then cross your thumb under onto the A. Cross your thumb under again on the E# and use your third finger to hit the F#. Coming down, hit the E natural with your second finger and the D natural with your thumb. Now cross the third finger over and continue down the scale.
The left hand fingering for the scale starts with your fourth finger on the F#. Continue playing until you get to your thumb on the B. Now cross the third finger over to the C# and play until the thumb hits the E#. Finish the scale with the second finger on the F#. To come back down the scale repeat the process. Be sure to remember to hit the E and D naturals instead of sharps.
For the next lesson, check out the F Sharp Minor Harmonic Scale.