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If you are playing in the Key C major, a chord progression can be as simple as C-F-G7-C or C-Am-F-G7-C.
What are the principles while using chords like Am7,Am6, Cdim7,Csus4,Cdom9,C13,Bflat,Aflat etc (many more which I have not written). When do you use these types of chord in the C major key? What are the guiding principles in the chord progression when these chords are also used in C major?
Okay, so you're talking about substitutions and passing chords in general. I'll try to handle both as best as I can. I'll deal with everything in C major as well.
Let's take a look at the most typical chords I, IV and V. Each chord in the key of C can be substituted with another chord. The I chord (CEG) can be substituted by VI(ACE) or III(EGB). Why? Because both III and VI share two out of three of the notes from the I chord. Now, something you have to understand is that not all substitutions sound good and your ear needs to be the ultimate judge in the end. I tend to sub I with III or VI, but I find that if the I chord is at the beginning of a phrase substituting it with III sounds very strange and modal. VI is a very nice (and dark sounding) substitution for the I chord. Let's take a look at another chord...the IV chord. The IV (FAC) can be substituted with II(DFA) or VI(ACE) since, once again, they share 2/3 notes with the IV chord. Personally, I almost never sub IV with VI because VI has more of a function with the I chord than the IV chord, but it is an option and something that you need to explore by trial and error yourself. V can be subbed with III or VII.
Extended chords like m7, M7, 7, 9 etc can all be used in conjunction with these substitutions. Let's say we substitute I (CEG) with VI (ACE), we can always use Am7 instead of Am. We can Am9, Am11 and many other variations. Each extension of the basic chords adds more dissonance to the chords. This is definitely another topic and I won't go into the details, but I will say that you should experiment. If you want to know more about this, post another question and I'll handle it more fully.
This is a more complicated topic. There are several approaches to passing chords and I'll discuss them separately.
1) Cycle of Fifths: The cycle of fifths occurs in the following way where -> means "goes to". The cycle of fifths is uni-directional. C->F->Bb->Eb->Ab->Db/C#->F#->B->E->A->D->G->C->F...and so on. When using passing chords you need to always think about where you're going in the music, not where you are. Let's take a phrase as an example to see how this works (each chord is 4 beats long).
C Am F G
In the cycle of fifths, what "goes to" A? E goes to A right? Right! We can borrow some of C's time and put a passing chord in between the C and the Am. What will that passing chord be? Well, it's going to be some sort of E chord since E->A. We get the following with C and the E chord sharing 4 beats in any combination (2+2, 3+1, 2.5+1.5, etc).
C E Am F G
What type of E chord can we use? We can use E major, E minor, E7, Em7, etc. In general, you can use any type of E chord, but not all of them will sound good. E major will always sound the best. Why? Pretend that we're in the key of A major. What would it's V chord be? E major. So E->A is a V to I relationship (perfect cadence), which is the strongest type of cadence. If we're in the key of A minor, its V chord is also E major since we generally use the harmonic version of A minor. Once again E to Am is a V to I relationship and a perfect cadence...very strong. Once again, you have to use your ear when using these type of passing chords. Major will never fail you, but experiment with other types of chords.
We can add passing chords to other areas in our original phrase. Let's add a passing chord to the F chord this time. Remember, in the cycle of 5ths C->F. The C chord is going to borrow time from the chord before it, Am.
C Am C F G
Let's put a passing chord going to G. Recall, D->G.
C Am F Dm G
This time I used Dm instead of D major, just to show that both can work.
2) Semitone Above Approach: This is a very jazz/gospel-based method. Let's take our example passage again. This method uses the cycle of fifths as well, except it uses the tritone of each passing chord instead. Let's add a passing chord to the Am chord. E->A. What's the tritone of E? Three tones up (or down) from E is Bb. So to get to Am we can use a Bb chord. Typically in jazz we don't simply use a plain-jane Bb major or Bb minor chord. More colouring is required for it to sound good, but you can use Bb major as well, it will just sound very tame. A typical type of Bb chord that will be used is a Bb13 chord. I'm speaking from a pianist's perspective when I describe this chord. Bb13 is Bb D Ab G (the 13) and usually C (the 9th) as well. Here's what we get:
C Bb13 Am F G
Upper structure chords (dominant 7th chords with certain combinations of the 9, 11 and 13) are used a lot for this purpose as well.
Anyways, I hope this is helpful. Feel free to probe for more if needed.
Cdim7 is used as a passing chord from Cmajor to Dmin7, as in:
Cmaj > Ebdim7 > Dmin7
Aflat has a dominant function in the key of C, so Ab is often used as a substitute for a dominant or subdominant chord, so instead of
Cmaj > Fmaj > Cmaj
you may use
Cmaj > Abmaj > Cmaj.
Additionally, Ab7 is often used to resolve to or reinforce G7 which is the natural dominant chord in they key.
Gmaj > C6 > Gmin7 > C9 > Fmaj
> F6 > D7 > G7 > C
One of many reasons is that the melody line contains some of the notes that occur in the particular chord, especially notes on the 1st and 3rd beats (in 4/4 time). Generally an underlying chord reflects the notes in the melody at that point. As Bob says, a lot of the examples are not strictly within the C major framework, so there could be many more answers.
Those are often just notes add to chords to give a musical piece depth. Jazz players sometimes talk about coloring chords in with added sevenths and ninths.
Am7 This is just a chord with a seventh added. Regular solution of seventh should apply with these chords as well.
Am6 Chords with sixths are usually passing chords where the sixth acts as middle man between two notes.
Cdim7 This is a chord commonly found when a seventh is added to the leading tone chord. The seventh is flattened and still has to resolve.
