Diminished Chords are not used often. They consist of these degrees: I, ♭III, ♭V. Diminished 7th chords add a VI degree to the Diminished Chord. Diminished 7th are so easy to remember because all you have to do is use one of the diminished chord patterns (shown below) and find the root note in any position of it. In other words, if you want a C diminished 7 chord, all you have to do is find a C in any place in the pattern. Let me show you.
Diminished 7th Patterns
Notice in this next example that the pattern moves up 3 frets and is the same chord, just a different voicing. If you didn't notice already, Cdim7 is the same as Adim7, F♯dim7, and D♯dim7. They are all just different voicings of the same chord. Once you find one of them you have found them all, and if you want a differnt voicing, you just have to move up 3 frets. It's that easy.
C, D♯, F♯, A diminished 7 Chords
If you want a plain diminished chord, all you have to do is remove the VI note, or learn a movable pattern (just like any other chord) as shown below. (R= Root note)