It would help greatly if you memorized the finger positions for the major scale. Know that a sharp(#) makes a note higher while a flat(b) makes a note lower.
Don't forget:
semitone/half note - one fret
whole tone - two frets
If you memorized the major scale shape, you would know it has seven - excluding the octave - finger positions (or degrees, if you're fancy). From now on, we will refer to these positions as 1, 2, 3, 4, 5, 6, and 7. Easy enough?
Since most scales are variations of the major scale, we must make amends. For example, the finger positions for the Natural Minor scale are 1, 2, 3b, 4, 5, 6b, 7b. Try to remember that in this format, a flat(b) means you go a fret lower and a sharp(#) means you go a fret higher.
C Major Scale C Natural Minor Scale
|------------------------------|------------------------------| |------------------------------|------------------------------| |------------------------------|------------------------------| |-----------------------9--10--|-----------------------8--10--| |------------8--10--12---------|------------8--10--11---------| |-8--10--12--------------------|-8--10--11--------------------|
C D E F G A B C C D D# F G G# A# C
1 2 3 4 5 6 7 8 1 2 3b 4 5 6b 7b 8
The Natural Minor Scale is a base for many other minor scales such as:
Harmonic Minor Scale
1 2 3b 4 5 6b 7 8
|----------------------------| |----------------------------| |----------------------------| |---------------------9--10--| |-----------8--10--11--------| |-8--10--11------------------|
1 2 3b 4 5 6b 7 8
Melodic Minor
1 2 3b 4 5 6 7
|----------------------------| |----------------------------| |----------------------------| |---------------------9--10--| |-----------8--12--11--------| |-8--10--11------------------|
1 2 3b 4 5 6 7 8
Familiarize these shapes and you will go far.