This is a beginner's tutorial which leaves out a lot, for example all about chord inversions and voicing in general. It shows my dirty working technique for melody accompaniment. It does not cover the finding of some fancy effect chord to prepare the song bridge or a scale change and other tasks like these. Please comment and add ideas. Show me your own chord finding trick.
Preface: don't believe the braggarts who claim that music is about emotion exclusively and therefore they need no theory at all. (In most cases the guys who told this to me weren't musicians themselves, but simply claimed know "someone very professional who says this".) Well, there may be geniuses on the one hand, and on the other in pure melody playing this might even be true for one musician out of 100. For normal humans like me I assert: there is no good chord finding without a little theory but simply with experimenting. There are so many chords available that without knowledge you will stick in the trial-and-error process eternally or will end up using boring or even wrong chords. (And yes: in some way "right" and "wrong" does exist in music. This is not about what any teacher says and his authority, but what you hear and what will make you and your audience have emotions.)
1. Find the scale root: forget the first melody note, look at the pitch of the last one! In most cases it indicates the root pitch of the key and scale.
You may skip paragraph 2 if there is any sheet available. In this case you may let the accidentals and something like the circle of fifths help you. But don't take the accidentals dogmatic.
2. Look at the other pitches of the melody, especially at the third and the seventh in relation to the root: is the third minor and the seventh too, then it is the minor scale. Third and seventh major: major scale.
3. Recall all the triads over the scale pitches: in every case take the pitch, its third and its fifth within the scale.
(If you don't know them, just draw five parallel lines and ad a key. Yes, this is one of the moments where music notation becomes helpful, no matter what any poser says. Throw the accidentals in and mark the pitches of the scale side by side, not above. Now mark over each marked pitch the following thirds of the scale, which becomes either line-line-line or gap-gap-gap.)
Examine these triads. There will be three major, three minor and one diminished. This is your universe for the beginning.
4. Work on the accentuated notes only, forget the other ones or think about them much later.
5. For every accentuated tone-pitch you may choose one of three possibilities: it may be the first (lowest), second (middle) or third (highest) pitch of a triad - of one of those you've found living within your scale.
6. Now you may simply go on by trying them three possible triads out for every accentuated note you'd like to harmonize. But keep your mind open for those few cases in which the sounding melody pitch may actually lie outside the chord triad. (Likely it is a seventh or even ninth in relation to the triad root pitch, which means if none of the three triads fits you may move down the triads you test a third, two thirds ...)
You can stop here and go on discovering. Have fun! Perhaps this is already enough for a music life. But maybe it is a little annoying to always having try three possible triads. Improvising musicians can't do it either. They know some further things. Follow the next step if you like:
7. More sophisticated would be to have a harmonic progression in mind: The song often starts with the I-Chord (with the scale indicating pitch as lowest triad pitch), then in some way moves to the V-chord and quickly returns to the I.
That would be it. Ok, if you wonder about some chords you find in songs, take this one:
8. For each major triad (with the major third) there waits a "relative" minor triad (with a minor third) as a replacement to make song smoother and more elegant. The minor triad always starts a minor third lower than the corresponding major triad. And reverse: a minor triad may be replaced by the related major. Songs in minor get fresher and stronger by these replacements.
That's it. Try the songs you know by using the replacement possibilities. After you know how to handle this you may read further. Refinement:
9. In a song based on a minor scale, the working V-triad (V-Chord, dominant chord) may be major, even if the pure scale says it should be a minor triad. Trust me, even if I don't want to explain it here. Let me just say: First is music, then the scales. Scales are theoretical ideas. Sounding music rules. Don't believe in scales.
10. Add some spice: try putting the minor seventh on the V's (dominants), maybe the major seventh on the IV's (subdominants). Extend it to the ninth. (the additional pitch always one further third above) On some chords there may be additional fourths and sixths (and here the deeper harmony theory would start). You may discover that if you spice up the related minor chords the effects will be different. A minor chord with a seventh integrates it's related major chord. The effect of the major's seventh would be done by the related minor's ninth. Got me? That's why you find the ninth more often with the minor chords.
11. Now be prepared for real music that doesn't fit into this micro-theory of making chords. Take "If I were a carpenter". Where does it start harmonically, where does it end? What is it's scale? Do not freak out if reality is more complex than this DIY, o.k? Enjoy it if a song defies this simple theory. There are so many progressions in beautiful songs that will not fit in here. Music theory has wondered ever since and created lots of words for all the cases. I-V-IV-I instead of I-IV-V-I is very mellow and mild. Highly likely it is the melody which demands the chords in this order, see rule number 5.
Some other things may happen. Don't worry, try out. Don't believe in the rules we already know alone. Here just one example where advanced harmony theory starts once again:
12. This is about power. Every (!) major triad with an additional minor seventh (dominant seveth) is a Dominant (a V-chord) and wants the corresponding basic chord to follow. This can change the scale of the song! One could emphasize this by saying the major-7-chords are the masters of harmony. They rule. So if in C-Major for example you add a minor seventh to the F-Major-chord, which would be the IV, then this F-Major-7 or "Fj" becomes a V-Chord (Dominant) which demands IT's corresponding (!) tonic, IT's I (or the relative minor replacement) to follow, which is not the C-Major anymore, but the Bb-Major. Other chords don't sound that good here. But as always there are exceptions. (I've met songs even ending on a dominant chord ot there in the wilderness) Don't fear them. Enjoy them, because herein lie a whole dimension of individuality and an exceptional form of beauty.
13. There may be double dominants. If you understand article 12, then don't have to wonder anymore if in C-Major there might be a D7 (major chord mith minor seventh) at some point. It should be followed by a G(7) which is the dominant. In this case the dominant had declared itself as the root triad (tonic) and carried with it's own related dominant, the D7. You may call this a short-timed scale change. This is nothing too special.
14. This is a reasonable point to start looking at the less accentuated notes, for example on the 2 and 4 in 4/4. Why not enhance such one a bit by a dominant according to that following chord at the next accentuated time.
15. Here we have already touched the thinking of targets. Every cadence is a movement towards a target and every cadence includes as it's main ingredient a movement from V (dominant) to I (tonic), no matter how disguised it might be. The target might be considered as always being a I (root triad, tonic) which is approached by it's related V (dominant). In a song there are some preliminary targets. One of them is the dominant. The above said means that this V if it is regarded as a preliminary target I is a I (tonic) in it's own domain. From this follows that a chord change into the dominant can be regarded as a smooth scale change or "modulation". (This is why it is no big deal to use the mixolydian scale of the dominant's root, what means you would indeed simply stay within the basic scale of the song, right?. To start thinking in chord-function-adapted scales you may simply take simply the major scale of the dominant's root pitch, because you have modulated into another scale. According to the basic scale of the song this would be the lydian scale. This idea of "changing the scale into the chord" is not universal, but to my opinion it opens the view into a less complicated and more practical thinking for beginners and lazy ones.) It is to the harmonizer's decision how strong to approach these targets. An approach puts some emphasis on the target. By the way this is what walking bass is also about.