what chord is it?

Let's assume that you've played some sort of harmonic structure and you want to know (for some reason or another) what's the name of this thing I just played? We've discussed before that context has a lot to do with a chord's naming, but for now let's say that we're just dealing with one chord that sounds really cool and we need some kind of name for it. Here's a method which can get you in the game:

1. Write out all the chord tones and remove any duplicated tones.

2. See if there are any triads present (might have to look enharmonically). If no triads
go to step 4.
(a) If there's just one triad then this is likely your chord: go to step 3.
(b) If there is more than one triad pick the one that makes sense to you and go to step 3.

3. If there are any remaining tones they will relate in one of three ways, as:
(a) extensions
(b) additions
(c) suspensions

4. If no triads:
(a) Is one implied (e.g. a major 3rd could imply a major triad)
(b) Is it a power chord?
(c) Is it a stacked interval (stacked 5ths)
(d) Is it a tone cluster?
(e) Does the harmonic structure correspond to/imply any mode?

Needless to say for the above to work we have to have some sort of knowledge of basic triads and extensions, etc. Let's take a few examples and see what happens.

Example 1: f, g, a, c#.
Are there triads present? Yes: f, a, c# is an augmented triad.
Any remaining tones? Yes: g. This relates to f as a 2nd or 9th. Since there's no 7th present (which would be some sort of e) let's call this an F aug add 9 (or F+5 add 9).

Also example 1 can be viewed like this: f might actually be e# enharmonically spelled. That means we would have an A augmented triad: a, c#, e# (f). The remaining g is simply the 7th, so the chord could also be named: A7+5. (This kind of enharmonic spelling is quite common in music, classical or otherwise as music is really a guide for performers and not analyzers.)

Example 2: f#, g, b. Any triads? No. Any triad implied? Yes: g and b can easily give the sense of a G major triad (the perfect 5th is not needed for the ear to hear the "complete" chord). Then f# is simply the 7th which gives us a Gmaj7.

Example 3: bb, a, c, b. Again, no triads, buuut...a and c are enough for an A minor triad. The remaining bs are 9ths: we could call this structure A min add 9 add b9. Clearly, though, this is a form of a chord cluster, which will never yield very willingly to a nomenclature born of tonal music.

Also these 2 rules will help from time to time:
(1) If you ever have both a major 3rd and a minor 3rd treat the major 3rd as the actual 3rd and the minor 3rd as a(n enharmonically epelled) sharp 9th. E.g. the tones e, g#, b, d, g can be viewed as an E7#9 (g = f double sharp).
(2) Similarly in cases where you have a perfect 5th and a diminished 5th the perfect 5th is the real fifth and the diminished 5th can be seen as a sharp 11: c, e, gb, g, b = C maj7 #11 (gb = f#).

If the above is of only the slightest help then it will have served its purpose: the sound of the chord (and its emotive evocations) is the most important thing; the importance of naming it lies somewhere between a distant second and not completely a worthless endeavor.

See also: triads, seventh chords, slash chords, sixth chords.