Do we have an accord?

First things first, I shall assume that virtually no prior knowledge exists. Let's start with intervals. In western music, we work with 12 tones. Some notes are what we call enharmonic meaning they sound them same on an even-tempered instrument (such as the piano/guitar).

A
A# / Bb
B / Cb
C /B#
C# / Db
D
D# / Eb
E / Fb
F / E#
F# / Gb
G
G# / Ab

The shortest distance between a note is a half-step. This may be represented by adjacent keys on a keyboard, or adjacent frets on a guitar. Let us examine these intervals using the key of C major. The notes contained in C major are as follows:

C D E F G A B (w w h w w w h)

The root note is C. The relationship between each note in the scale within 1 octave, and the root note, is as follows:

C - C = Unison
C - D = Major 2nd (1 step)
C - E = Major 3rd (2 steps)
C - F = Perfect 4th (2 1/2 steps)
C -G = Perfect 5th (3 1/2 steps)
C - A = Major 6th (4 1/2 steps)
C - B = Major 7th (5 1/2 steps)
C - C = Octave (6 steps)

If you lower a major interval by a 1/2 step, it becomes a minor interval. The reverse is true, thus if you raise a minor interval by a half step, it becomes a major interval. Let us rearrange the notes of C major, starting on A. This gives us the key of A minor.

A B C D E F G (w h w w w h w)

A - A = Unison
A - B = Major 2nd (1 step)
A - C = Minor 3rd (1 1/2 steps)
A - D = Perfect 4th (2 1/2 steps)
A - E = Perfect 5th (3 1/2 steps)
A - F = Minor 6th (4 steps)
A - G = Minor 5th (5 steps)
A - A = Octave (6 steps)

Thus, we see what defines the relationship between 2 notes is their distance from each other, and how rearranging the order of the notes gives us a different sound.

Let's now consider how this applies to chords. A chord is usually made up of 3 or more notes. These notes are usually stacked in thirds on top of a root note. These thirds may be either minor or major thirds. So, for a triad, the following configurations are possible

1 - 3 - #5 = Augmented
1 - 3 - 5 = Major
1 - b3 - 5 = Minor
1 - b3 - b5 = Diminished

Applying this with a root note of C, we would get

C E G# (C augmented)
C E G (C major)
C Eb G (C minor)
C Eb Gb (C diminished)

Let us take this further and apply it to 4 note chords

1 - 3 - #5 - octave = Augmented
1 - 3 - 5 - 7 = Major 7th
1 - 3 - 5 - b7 = Dominant 7
1 - b3 - 5 - 7 = Minor/Major 7th
1 - b3 - 5 - b7 = Minor 7th
1 - b3 - b5 - b7 = Minor 7th flat 5th / half-diminished
1 - b3 - b6 - bb7 = Diminished 7th

Of course, there are many other kinds of chords. One might construct chords by stacking in 4ths, or by adding colour tones such as 9ths/11ths/13ts (which are 2nd/4th/6th intervals an octave above the root), or just replacing the 3rd with a 4th or major second, creating suspended chords, as some examples. Experimenting is the key to success!

As for chord substitutions, here are some brief pointers:

For any diatonic chord, one may substitute a dominant chord with the same root note. We call these secondary dominants. They're extremely common in jazz and blues. Dominant chords create a dissonant sound that wants to be resolved, so be careful using these when you're going for a "smooth" sound!

For any dominant chord, we may substitute another dominant chord that is a tritone (flat 5th) away. This is because of the structure of a dominant chord. Let us use E7 as a example.

The notes of E7 are E G# B D

If we move up a tritone, we get Bb7, which has the notes Bb D F Ab

Notice that in E7, the G#/Ab is the major third and the D is the minor 7th. However, in Bb7, the G#/Ab is now the minor 7th, while the D is the major 3rd. Because it's the major 3rd and minor 7th that give the dominant chord it's tonality, we can use these chords interchangeably.

If you're wondering why this works, a tritone divides an octave exactly in half. The major 3rd and the minor 7th are also a tritone apart, thus, when we move up a tritone, these notes swap functions. A pretty nifty trick!

Lastly, we come to inversions. Let us consider the case of C major 7. By rearranging the notes, we have different inversions of the chord, and this is the gateway to substitutions. Next to the chord is a chord that may be substituted for it, along with how the notes that have been changed/added affect the CM7 chord

C E G B - CM7
E G B C - CM7/E -> Em7 - E G B D (D is 9)
G B C E - CM7/G -> G7 - G B D F (D is 9, F is 11)
B C E G - CM7/B -> Am7 - A C E G (A is 13)

To simplify, for any major chord, you might substitute a minor chord a major 3rd up or a major 6th up. The reverse is true. Play around with this and see what kind of sounds you like. As you've probably figured out by now, the possibilities are endless!

NB: I don't have "formal" music theory training so some terminology might deviate from the norm. Hopefully you find this useful though!