A melody or series of notes is diminished if the lengths of the notes are shortened (this is opposed to augmentation, where the notes are lengthened). A melody originally consisting of four crotchets (quarter-notes) for example, is diminished if it later appears with four quavers (eighth-notes) instead. This technique is often used in contrapuntal music. It gives rise to the "canon in diminution", in which the notes in the following voice are shorter than those in the leading.
An interval is diminished if a minor or perfect interval is narrowed by a chromatic semitone; a diminished chord is constructed of stacked minor third intervals. Thus a diminished fifth, for example, is a chromatic semitone narrower than the perfect fifth, and a diminished triad consists of root, minor third, and diminished fifth.
An example of a diminished scale would be A Dim - A B C D D# F F# G# A Diminished Scales are very easy to construct, you simply start at your required root note, and from there just move up a tone and then a Semitone, continue this until you have your scale.
Root/ Tone/ Semi/ Tone/ Semi/ Tone/ Semi/ Tone/ Semi
A B C D D# F F# G# A
From there you can form a diminished chord by using the A, C, and D# (root, minor third, diminished fifth). In a diminished chord you have 4 notes which are each a successive minor third apart, leading to minimal transposition. So there are actually only 3 different diminished chords (e.g Cdim contains the notes C, Eb, F#, A, as does the diminished chords with the roots of Eb, F#, and A)