: Augmented chords and chord substitution? Say we are in C major; how do we use chords like the Augmented chords, other diminished chords outside the scale (minor to major substitution, dominant 7th substitution, altered chords,

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Any major chord can be converted to an augmented by raising its 5th. On the same fashion, every minor chord can be converted to a diminished by flattening its 5th. Since both chords are dissonant they provide tension which tends to be resolved either to their "parent" chords (from which they became ex. C-E-G becomes C-E-G# and then the tension is resolved back to C-E-G) or to a different chord which shares some common tones (ex. C-E-G becomes C-E-G# then the tension is resolved to C-E-A which is an Am).

One heavily used example of the diminished chord (apart from the VII degree of the harmonic minor scale) is the diminished chord built upon the raised 6th degree of the minor scale. For example, in the A minor scale, one can substitute the Am (A-C-E) chord with an F#dim (F#-A-C) or combine them to create an Am6 chord (A-C-E-F#).

Although both chords tend to give a sense of departure from tonality only the diminished chord is widely used.

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There are many ways to utilize chords outside the key and many ways to approach how to use of each individual chord you list. Like always, you would want your melody and harmony to be compatible in that if you have a melody the harmony you create should reflect that and vice versa. Even though there are many ways to approach using these chromatic chord and others like it, they typically fall into one of the three categories below.
Passing
The point of these chords are just to get from one chord to another in a chromatic fashion typically with one or more notes chromatically moving up or down. The augmented chord is a good example of this where in the key of C we can use the chord progressions:

C -> C+ -> Am

In this progression the C and E are common in all chords and the notes G-G#-A chromatically ascend. The melody could outline the either the common tones or the chromatic line. Both have different effects and I recommend try both to see the effects.
Borrowed
In this case we're just temporarily borrowing a chord from a neighboring key or mode and continuing in our key like we normally would after the borrowed chord. In the example below, we are in the key of C major and we're borrowing Fm from C minor.

C -> Fm -> Dm -> G7

Again pay attention to common tones and there is still a chromatic ascending line you could take advantage of when writing a melody for the progression.
Another way to borrow chords from other keys which have a secondary function. The most common chords of this type are secondary dominants and in the example below we are using the dominant of the key of G major in the key of C.

C -> D7 -> G7

Pivot (move to a new key)
In this case we'll use a chord outside the key to move to a different key. Dominant chords like a dominant 7th or a fully diminished 7th are very effect for doing this especially when the new key is far away, but other chords outside the key could be used to start the pivot away from the old key and into a new key. In C, a very simple example would be:

G7 -> Bo7(D#o7) -> E

In this we're starting with the typical dominant chord in the key of C, G7, and we turn it into a fully diminished chord by raising the G to a G#. One of the properties of a fully diminished chord is

There are many ways to use the same chords to get different effects and you'll need to experiment and take note of what progressions, substitution, and chromatitizim works in what scenarios, but they will mostly likely be fall into one of the categories above.