If I sit down in front of a piano, how do I arrive at the minor/major scales?
Simple answer for a simple question.
Find C on the piano (white, left of two blacks).Play each white consecutively. That's C major. By moving each and every note up by the smallest degree possible ( one semitone), that will give C# major. This will continue for each of 12 keys.
Or - note (sic) what the jump is between each of those notes in C. That pattern transfers for each different start note, so producing each scale.
Start on A instead, and there are the natural minors. Give a man a fish...
Here's two clutter-free tutorials on how to construct the Major and minor scales:
If you still find it hard to follow, I highly recommend you to check out all the basic music concept lessons on this site that come before introducing scales. You should at least acquaint yourself with notes and intervals before proceeding to think of scales.
Major and minor scales are based on the pattern of intervals between the notes. Where
W is a whole step and
H is a half step,
W W H W W W H
Natural minor scale:
W H W W H W W
This is why, as Tim pointed out in his answer, if you take a major scale and move every note up a half step, it's still a major scale; the distance between the notes stays the same, even though the notes change.
There are actually several different minor scales in each key, but even so, they all are constructed according to the number of half steps between each note. Each of the seven steps in the scales common in western music will have either 1 or 2 half steps between its note and the one before. If you learn those characteristics you can play a major or minor scale starting on any note.