Secondary Dominants are an important harmonic function that will help you understand modulations and some chords that 'don't seem to belong' in the key. I assume you know and understand the diatonic chords (chords in a key) and can work them out easily.
So we know that the V chord in the key of C Major is the Chord G7, and it pulls to it (see the lesson on Functioning Dominants for a full explanation), and the V-I motion can be applied to other chords in a key as well!
Let look first at the Chords in the Key of C.
The a V chord can precede any chord, major or minor. What we want to find is the V chord that leads to the chord built off each degree of the scale!! The V chord that leads to the I chord? Well, we already know that! That will be G7 going to Cmaj7...
But what about the V chord going to the ii chord, the Dmin7? Or another way of asking - what would be the V chord in the key of D? (remember it makes no difference if the chord is major or minor!). So?
The answer is A7, the V chord in the key of D. So we would say that the Secondary Dominant of the (ii) Dminor is A7. This would be written as V/ii or said "the five of two". You will often see an A7 in the key of C, most often followed by the Dmin7... even the I-vi-ii-V progressions we looked at previously often went C, A7, Dmin, G7.
The pull of the V going to I is very important and very strong, so much so that it doesn't really feel like a modulation (key change) but just a subtle shift in the harmony.
So lets continue... what would be the V chord of the (iii) Emin7? What would be the V chord in the key of E? That's right... a B7.
So the B7 chord is the V/iii, the five of 3. This is also a lovely shift used a lot in pop and soul. One of my personal favourites.
So the Fmaj7, what would be the V/IV, the five of four??
I remind you here that it's often easiest to do this stuff on tech guitar neck and the more familiar you get with doing it that way the faster you will get at it. I've found that I see the guitar neck in my mind and can do quite complex 'calculations' very quickly using a somewhat visual approach!
The V/IV is C7! A very cool change this one, so when you are going from a C to and F you can tickle a little C7 in there to spice things up a bit. Really? Listen to it. Try it. It HAS to sound good. Sometimes it will, sometimes it won't. With all these things you have to keep your ear open.
Now we're at the V of V. Yep, the V chord that leads to the V chord... so which is the V of G? That will be D7.
Only a couple left. The V of vi? the V chord that goes to Amin7?? E7. This is an awesome one too... it's the chord that will often lead you to the key of A minor. In fact if the song starts on Amin and uses mostly chords in the key of C but with the occasional E7, you are most likely in the key of A minor (see Demystifying the minors lesson!).
The last one, well it ain't used much to be fair. The V of vii... the V chord that goes to Bmin7b7? It's F#7, about as far from C tonality as we're going to get in this and it sounds pretty out too. There are some tunes that use it but not a whole lot.
So lets re-cap on what we got.
|V / I||V / ii||V / iii||V / IV||V / V||V/ vi||V / vii|
Remember that 'usually' the secondary dominant will resolve to it's I chord, but it doesn't HAVE to... that's the beauty of all these rules, they are made to be broken :)
But what you should find very valuable is looking at jazz standards now with this information and trying to spot all the Secondary Dominants that you can. Will learn a lot in the process...
These chords are often used as pivot points for full modulations too, but that is another story and shall be told another time!