Diminished is actually the name of a chord and a scale.
The diminished scale in C contains for example the notes
C, Eb, Gb (and A).
The scale contains C, D, Eb, F, Gb, Ab, A and B.
The diminished tuning for diatonic harmonicas has the same order of notes (with the typical whole note / half note structure).
This structure makes it possible to reach all chromatic notes with the help of the bending technique alone. It is not difficult to learn, but exact intonation needs a lot of practice.
The advantage over regular chromatic harmonicas (which can be tuned in diminished as well) is in my opinion the more powerfull and dynamic sound of the diatonic Diminished.
The ordinary 10 hole Blues harmonica is tuned according to the Richter-System. It is designed to play songs, which remain inside the harmonic setting of one scale. Other songs in other keys require more harmonicas. To cover all 12 keys, the average Richter player needs (at least) 12 instruments.
For songs with more complex chord changes (appearing in genres like Jazz, Tango, Latin or even some Pop and Rock songs), the Richter tuning is extremely hard to handle.
My recommendation: everyone who is interested in playing these styles should give the dimished tuning a try.
The basis of a fast and pleasant learning process is surely a decent instrument. Harmonicas of a poor quality make intonation and dynamic playing twice as hard.
At first, the beginner should learn how to play single notes.
Then the bending of the draw notes has to be managed. The lowest and the highest
notes are the most difficult ones and even for the advanced player not easy to master.
After a while you might want to play simple melodies, for example children's songs, national anthems or (slow) Jazz standards. Try to play every note nice and clear. The starting point of the melody is not important. They are all more or less of the same difficulty. You might even learn some licks in all 12 keys to use them in some of your solos later.
It is quite likely that the first attempts on the Diminished sound strange. You will surely need patience and practice to master it.
In my opinion the minor pentatonic is the most important scale for inexperienced players. It is extremely versatile and can be used in almost every musical style.
Minor pentatonic in C (including half note steps):
C (3) Eb (2) F (2) G (3) Bb (2) C
|C minor pentatonic||D minor pentatonic||G minor pentatonic|
I propose the major scale as the second one to learn. It is helpful to study its structure well, because other scales contain exactly the same notes. C major, D dorian, E phrygian and F lydian for example have only different root notes and are in other respects identical.
C major scale:
C (2) D (2) E (1) F (2) G (2) A (2) B (1) C
|C major scale||D major scale||G major scale|
This should be enough as an introduction. I hope it helped to get to know the diminished tuning better.