Q:

Intervals confusion

If we need to find the note which is a major 6th below G (which is a Bb), do we find it using the major scale of the top note (in this case G) or the major scale of the bottom note ( in this case Bb). Is it the bottom note (Bb) as G major does not have a Bb whereas Bb major has a G?

A:

My understanding is you: 

first get the interval number (second, third, fourth, fifth, sixth, seventh, etc.) by stepping through pitch letters (A, B, C, etc.)
then determine the interval quality (major, minor, augmented, etc.) and this determined by the number of semitone between the two notes.
you may need to enharmonically re-name the second note to maintain the correct pitch class and lettering.

Example, a minor third above G: the third letter above G is B, a minor third is 3 semi-tones - stepping up we go G#, A, A# - we want a B and so enharmonically name A# to B flat.
That is a tedious process. So, probably most people use more practical shortcuts. On some instruments like keyboards and fretboards people probably end up learning 'shapes' of intervals. In a major key DO to MI is a major third, lower it a semitone to get a minor third. On a piano two white keys with two black keys in between will be a major third. Eventually you do this without really thinking about it. Sometimes you need to stop and think through intervals like augmented second, augmented sixths, or the use of double sharps and flats typically when the scale tonic is a sharp or flat (like c# minor or D flat major.)

