Chords can be a lifetime study, and a lifetime isn’t long enough to learn them all. To make matters worse, there are seemingly endless ways to play the exact same chords on your guitar. Most guitarists use about 3% of what is out there, but with some basic theory knowledge we can understand how to use them in our music. Understanding the rules will help us make better, faster choices when soloing, and there won’t be a need for so much ‘hunting for the right note’ when constructing solos.
All examples here are recorded with the Seymour Duncan Custom Custom bridge pickup. I use this in an unusual guitar: a maple and graphite Steinberger. The Custom Custom is great for brighter guitars because of its focused mids.

Like many of SD Pickups, the Custom Custom is available in a variety of colors.

To start, let’s look at the qualities of specific chord types. Two of the most common are major and minor chords. Here are some major chords:

Notice how happy and bright they sound. To contrast, here are some minor chords:

Notice the sad, darker sound.
To be fair, we’ll also talk about another quality of chord, the diminished chord:

This doesn’t sound happy or sad, but it holds ‘tension’ – this unsettling feeling that there’ll be another chord afterwards.
In the last Breaking Down the Barriers post, I talked about half steps and whole steps. If you start on the letter C, and use the formula for the major scale (in steps, 1  1  ½  1  1  1  ½) we get:

C D E F G A B C

We derive the first chord by starting on C, then jump to the E, then jump to the G. These are the 1^st, 3^rd, and 5^th letters. You can see we are using every other letter (3 letters for now). This is called a C major.  Now we guitarists usually just call it a C chord. It is easy to visualize on a piano keyboard as well.
The 2^nd chord starts on the D, and yes, we use every other note: D F A. This is a D minor. Or Dm. If we continue with this, we end up with 7 chords:

C  Dm  Em  F  G  Am  Bdim

These are the 7 basic triads of the key of C. Why should we care about this? As guitarists, we may want to construct a solo. And to do this, we need some sort of harmony chords in the background. This formula gives us 7 basic chords to base our song on. We don’t have to use all 7. We can just use 3 if we want. We don’t even have to start with C (also called the tonic chord), but for our purposes now, we will.
Side note: As stated above, each of these chords contain 3 notes. Thing is, you can double, triple, quadruple, etc. any of these letters in a chord. And they can be in any order. However, if you add any letter other than an C, E, & G to an C chord, it ceases to be an C major and we have to give it another name.
Now, to make things more interesting. Triads are 3 note chords, and the building blocks of western harmony. What if, we decided to extend these triads to 4 note chords? Let’s go back to our original notes:

C D E F G A B C

If we chose C E G to make a C chord, what would happen if we chose another letter? And which letter to choose? Well if C E G are the 1, 3, & 5^th notes, the next logical note to choose would be the 7. Adding a B to a C major changes the name of the chord. It is no longer a C major, it is a C major with an added 7. This is now named a C major 7. Or Cmaj7 in guitarspeak.
Making each chord 4 notes, we end up with slightly different chords:

Cmaj7  Dm7  Em7  Fmaj7  G7  Am7  Bm7b5

I can pick both 3 and 4 note chords to construct my chord progression. Something like Cmaj7, Dm7, Am, G7 would work.

This gives us some chords to base our solo on. What notes do we play? The notes we play come from the C major scale which we learned above. It is up to us to come up with something interesting, but no soloists start out playing their best- they have to work hard to get where they are. Fortunately, understanding this system of constructing harmony is very helpful in isolating the notes which will work and those which won’t. Of course all rules are made to be broken, but it is better to break them because you intend to, not because you don’t know any better. And you don’t want your keyboard-playing friends to snicker at you.