Hope this helps a bit.
A diminished scale is pretty limited but can be used melodically over diminished harmony which mean dminished chords. (Your teacher might prefer f-flat to my E-nat near the top for technical purity but I'm trying to keep it easier).
Nicki, the first scale you mentioned, based on G should look like this. It relates to the diminished chord that, as shown, has 3 "inversions".

There are only 3 different basic diminished chords (so far as the notes in each one go)
(Please note this isn't technically correct but from a practical/musical view it's best to see it that way now).

(I'd better mention it - someone will - they are derived from chord vii (the triad based on degree vii of any diatonic scale) with a dim7th added on top. Don't worry about that right now. And strictly, there should be 7 letter-names of notes in a 7th, so my G(bass) to E (at the end of the above line & elsewhere) is inaccurate - the E should be an F-flat to the purist)
Since there are only three different diminished chords, each one can be used in 8 different keys, 4 major and 4 minor.
Here's the one we first looked at resolving onto 4 associated MAJOR keys. You don't have to stick to the inversions shown but they're best in this setting.

All of which makes modulation to remote keys dead easy.
There are several ways. But if the (diminished) chord appears in both old and new keys, you move off the old key onto it...then move into the new key. The theoreticians call it a pivotal chord. There're also tech words for leaving and getting into the new key - no more space here for that. This post will prob get deleted as it is....
Anyway, here's an example modulation:
(note: the notation of the vii chords isn't quite correct - sorry the 9s are meant to be dim 7ths.)The whole subject of dimished chords, how they're derived,used and so on, is quite big but this little lot should help place what a "diminished scale" is. Use it to solo above a diminished chord. There're also lots of nice suspensions to and from these chords.
>>>>Note, I was more concerned to put something up that people could play and see on music paper. Any questions or comments about intervals, please PM.
Cheers,
R