To learn the diminished chords, all you do is lower the second and third notes of the major chord a half step. For example:
The C major chord is (C, E, G), so the C diminished chord is (C, Eb, Gb). The second and third notes are lowered a half step to Eb and Gb.
The F major chord is (F, A, C), so the F diminished chord is (F, Ab, Cb). The second and third notes are lowered a half step to Ab and Cb.