There is a difference between learning the finger pattern and learning the notes in a given key. The former is very instrument specific (and tuning specific) while the latter is the same for all instruments.
There are only 7 letter names for notes in Western music and they are A, B, C, D, E, F, and G. They are repeated over and over.
The "natural" notes, i.e. no sharps or flats are the same as the letter names previously given. The Natural scale is C major and is C, D, E, F, G, A, B repeat.
This scale has the interval structure of w-w-h-w-w-w-h where w = whole, h = half. Notice that this is really a 3 interval pattern (w-w-h) repeated twice with a -w- step between them. The group (w-w-h) is a tetrachord (4 notes, 3 intervals).
On the guitar each fret spacing is a half step. So going from 2nd fret to 3rd is a half step up, going from 10th fret to 9th is a half down.
All scales, or modes, can be expressed in terms of -w- and -h- steps and -h-is one fret increase while -w- is two frets. This assumes the formula describes an ascending scale which is the standard. The natural minor scale is w-h-w-w-h-w-w. You can apply this starting at any fret. No need to refer to accidentals. The name of the note you start on is the name of that major scale. Same for Major scale with w-w-h-w-w-w-h. Start on Eb and you have the Eb major scale.
Now, if you want to figure out the correct way to write the scale in SMN, figure out the note names with accidentals, then there are a few more things to be aware of. (1) We don't mix flats and sharps in the same key. (2) We don't use jumps of a 3rd for consecutive notes. In other words all scales are a 7 letter string of the alphabet sequence (A, B, C, D, E, F, G, A, B, C, D, E, F, G, ...). So start with the first letter name, then write down the sequence of letters, now as you walk up the letters decide if the next letter represents the -w- or -h- you need and if not adjust it with a # or b respecting rule (1). That should work.
As an example try Eb minor. The starting note is Eb, letter name E. The sequence must be (Eb, F, G, A, B, C, D, Eb) and we need w-h-w-w-h-w-w. Next letter is F and F is 2 frets above Eb (a -w- step) so leave it alone. From F to G is a -w- and we need a -h- so put a "b" after G. Notice how we now have two flats. F# is enharmonic to Gb but the sequence (Eb, F, F#) would not be proper form. Now from Gb to A is three frets (a minor third) and we need a -w- so flatten it. So far (Eb, F, Gb, Ab, ...). Next letter is B and that is 3 frets from Ab so once again we flatten it to make a -w-, (Eb, F, Gb, Ab, Bb,...). Now we need a half step from Bb to a C and the interval between those notes is a -w-. So we much flatten the C, yes you heard right. That gives you (Eb, F, Gb, Ab, Bb, Cb, ...). So, why not just leave it a B natural? Again, not proper form, the scales are always an unbroken 7 letter subset of (A, B, C, D, E, F, G, A, B, C, D, E, F, G, ...) with no repeats. To finish it off we need a -w- from Cb to a D. There are 3 frets from Cb to D so we need to flatten D to fit the pattern giving
(Eb, F, Gb, Ab, Bb, Cb, Db, Eb) = Eb minor
There are 2 natural semitones in the key of C, (E, F) and (B, C). If you follow the rules you can figure out the scales.
For a guitarist one of the amazing things is the "movable" chord and scale patterns. I am not suggesting you don't learn to read as that is important, but the movable patterns are equally important. They allow you to change key on the fly while reading by moving to the appropriate location, all other patterns being equal. This is not the only skill to develop, one should also learn to play all keys in the same position. But at a moments notice you can read everything as if it were in C by moving the C-movable form to the correct location and simply reading the notes as if they were in C. Makes life very easy.
Not sure if you started learning these patterns but a popular minor scale fingering is
(1, 3, 4) on the E string
(1, 3, 4) on the A string
(1, 3, 4s) on the D string
(1, 3) on the G string
(1, 2, 4) on the B string
(1, 3, 4) on the high E string
The notation is as follows, you have 1 finger 1 fret from 4 consecutive frets at any location. Then just put the fingers down in the order listed. The 4s on the D string mean stretch and you need to reach for a -w- step there. This is not the only way to play the minor scale. Playing this starting on the 5th fret (standard tuning) would be A minor, 9th fret would be either Db minor or C# minor.
I'm adding to this to address Tim's comment on harmonic and melodic minor. The German H is not addressed. The algorithm above works for the diatonic modes, Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian (natural minor), and Locrian. And it works for figuring out key signatures. You will not find mixed accidentals in these scales or the key associated with them. Harmonic minor has a sharp 7th (relative to its natural state) and Melodic minor has a sharp 6th and 7th ascending and a natural 6th and 7th descending (again, relative to its natural state). These minor scales can be constructed from the natural minor by adding a # to the appropriate notes. And as Tim points out this will necessarily create a mix of flats and sharps in those scales. However, these are treated in SMN as accidentals. Music in the key of A minor may use melodic minor but you will not find a G# and/or F# in the key at the beginning of the piece. The key of A minor has no sharps or flats. There may be exceptions I am unaware of but I've not yet seen a harmonic or melodic minor key signature.
In the example I gave, building the Eb minor scale, the harmonic version would be (Eb, F, Gb, Ab, Bb, Cb, D, Eb). Still no mix of # and b. But G minor for example would be (G, A, Bb, C, D, Eb, F, G), and the harmonic minor version would be (G, A, Bb, C, D, Eb, F#, G).