It is important to understand how a minor scale is made up. Remember a tone is a two fret move and a semitone is a one fret move. A minor scale is made up of 8 notes, the 8th note being the octave. Usually books will write the steps of the scale in roman numerals like this ( I - I - III - IV - V - VI - VII - VIII ). To modernise this we will just use the numbers 1 to 8 ( 1st - 2nd - 3rd - 4th - 5th - 6th - 7th - 8th notes of the Major Scale) or just ( 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 ). Then we place the correct spacing between each of those eight notes, remember <T> = Tone, and <S> = Semitone.
Formula For A Minor Scale
1 <T> 2 <S> 3 <T> 4 <T> 5 <S> 6 <T> 7 <T> 8
NOTE: the numbers shown in the diagram to the left are the order numbers (1st, 2nd, 3rd, & 4th notes of the scale an so on) and not your finger numbers.
As you can see below both scales would be an A minor scales if they were played from the 5th fret. The root note which is marked by the darker circle is placed on the "A" note, it's that simple. So when you learn the shape of a minor scale on the guitar, you have learnt every minor scale e.g. ( A, A#, B, C, C#, D, D#, E, F, F#, G, G#, A ). The name of the scale changes, depending on where you start the scale from.