Music Theory for Self Taught Musician
[Part One] The "skinny" on scales:
Written music is based on the piano keyboard, where each black key has two names. It is sharp to the key on its left and flat to the key on its right. So, for example, the black key between the notes F and G may be called F# or Gb.
A person who has perfect pitch, will argue that the relationship between notes isn't linear and that F# is, technically, a different note from Gb and that's all well and good but both are represented by a single key on the piano and are treated, musically speaking, as the same note.
There are 5 black keys on the piano and their 10 names are as follows:
Note: just as wind, reed and brass instruments each have a natural key, the piano has a natural key, that being specifically, "C", thus when you're discussing piano notes, as confusing as it may be, the "alphabet" begins with the letter "C".
The logic behind scales is one of expedience and couldn't be simpler to comprehend. For example, most anyone who's musically inclined can pick out the notes of a given scale on the piano by ear but, if the key isn't "C", where all the notes are white keys, our hypothetical musically inclined individual my not know what to call the black keys. Once you know the rules, it couldn't be any easier. The rule for scales is: Each note, except the one which begins your scale, can only be used one time. That's it, it's really that simple, for example a C scale consists of the notes C,D,E,F,G,A,B, and C. The note C, which begins the scale, is the only note that's used twice; no other note may be used twice.
When you raise a note by one fret on the guitar, or one key (regardless of color) on the piano, that is considered a musical "half step". Two frets, or two keys on the piano, is then a musical "step".
A scale has a simple formula. From its first note, the scale is assembled by raising the notes in the following sequence; step, step, half-step, step, step, step, half step.
[Lesson One - Review] This is important so I'll go through it again:
The RULE (for scales): You can have only ONE of each note, except the note you start on.
In other words, a C scale has a C at the beginning and another at the end, but only one each of the notes in between (and this is a universal truth).
Regardless of the key, from the first note, you can extrapolate the rest of the notes in the key by advancing in the following sequence:
first note 
step to note two 
step to note three 
half-step to note four 
step to note five 
step to note six 
step to note seven 
half-step to note eight 
Note: The first interesting observation you should be able to extrapolate from this is the the 7th note of any scale is but a half-step below whatever key you're in, thus, in the key of C, the note B, a half-step below C, is the 7th note of the scale. In some cases this truth can be used to tell you whether or not the key you're in is a sharp key. For example, in the key of G, the 7th note of the scale has to be the black key just to the left of the note G and, you can only have 2 Gs in the scale (see The RULE, above) thus you must call this black key an F# so the key of G HAS to be a sharp key. Do you see how clever that is?
What else do we now know about the key of G? Nothing yet, be patient.
Ok, now let's figure out the notes of that G scale and let's just go ahead and start thinking of the notes as numbers because that's going to be an extremely useful habit. We'll begin with a G so that makes it #1.
2. Step to A
3. Step to B
4. Half-step to C
5. Step to D
6. Step to E
7. Step to F#
8. Half-step to G
Now, having "mapped it out" we know that the key of G has one sharp, that being F#.
I always use the keys of F and G to explain this concept because neither is complicated. So, now let's map out F.
2. Step to G
3. Step to A
Here's where the magic happens. A half-step above A is a black key. We can't call it an A# because that would break The RULE (can't have more than one A) so it can only be called a Bb, ergo...
4. Half-step to Bb
5. Step to C
6. Step to D
7. Step to E
8. Half-step to F
So, the key of F has one flat, that being Bb.
In each case, the choice between sharp or flat was simply a matter of expedience, or, more accurately, following The RULE. :)
I'll leave you to tinker with the concept, with other keys, but beware, you'll find some keys which just don't work at all well, and, in some cases you'll have to call things by odd names to make the key work at all. Think of it as the awkward secret of the music industry. I'll give you one odd example: Because the key of C is composed entirely of natural notes, the key of C# must, therefore, be composed entirely of sharps, seven of them, in fact. In order to make the key of C# "work", you must refer to the note C as B# and the note F as E#.
[Part Two] The "skinny" on chords:
When you combine the 1st, 3rd and 5th notes of any scale they form a basic chord which is called a "triad" and bears the same name as the scale. If you add the 8th note of the scale to the triad you've created what is called a "full chord". If you combine the same notes in any other order or combination, you create what is called a "raised chord". All chords on a guitar are raised chords but there are instances where natural full chords occur on the guitar. For example, if you'll mute your E strings and play an open C chord (with only the inside four strings sounding) you'll be playing a full C chord. Muting the 5th and 6th strings when you play an open E chord will result in a full E chord. Ironically, especially in the case of the E chord, the 6 note, raised, open E chord is fatter (i.e. more full sounding) than the full chord.
Referring back to the piano keyboard, if you begin with an A and play successively higher pitched white keys, in order, until you get to the next A you will have played an A minor scale. In other words, it's the same notes as a C scale, just started (and ended) at a different point. In fact, the A minor scale has the same key signature as a C scale and this is why the A minor scale (or chord) is referred to as the "relative minor" of the C scale (or chord). Every major scale (or chord) has a relative minor. As with a major scale, if you combine the 1st, 3rd and 5th notes of a minor scale you will be playing the minor triad which bears the same name as the scale and adding the octave (8th note) forms a full minor chord.
The relative minor scale of a given major scale begins with the 6th note of the major scale. To find the relative minor chord of given major chord, either count alphabetically to the sixth note of the major scale bearing the same name as the major chord OR mentally figure out what minor chord is three frets below your major chord. For example, the relative minor of G is Em. The relative minor of C is Am. They're easy to figure out once you get the hang of it.
Chords within a given key (numbers as notes):
There are six triads which occur naturally within any given scale. The best way I know to exemplify this concept is to go to a piano (literally) and place the thumb and two fingers of your right hand on a C triad (i.e. the notes C, E & G) somewhere in the middle range of the keyboard. Keep your hand rigidly in the shape it assumed to play this chord, now lift your hand and move your rigid fingers one white key to the right (to the notes D, F & A). Play the chord, listen to it. Your fingers are now playing a D minor triad. Lift your hand and move your fingers one more key to the right (to the notes E, G & B). Play the chord. This is an E minor triad. One more key takes you to an F triad (the notes F, A & C). Another key takes you to the G triad (G, B & D). One final key takes you to an A minor triad (the notes A, C & E). So the family of chords which occur naturally in the key of C are, in alphabetical order, C, Dm, Em, F, G, and Am. These are chords based on the first six notes of the scale. Chords based on notes 1, 4 and 5 of a major scale are major chords while chords based on notes 2, 3 and 6 of the same major scale are minor.
If you work out the relative minors of F and G you'll find that they are Dm and Em respectively, thus it can be said that the natural chords which occur in the key of C are major chords based on the scale's first, fourth and fifth notes along with each of their relative minors and this is, then, universally true of any major scale.
Numbers as chords:
Using the so-called, Nashville number system, each key (scale) had 7 chords and they're ALL major chords by default. This isn't a rule, as such, it's merely a convention that makes it easier for musicians to communicate with one another in real time. In fact, one of these chords isn't even a part of the scale. The 7 chord, in the number system, isn't the actual 7th note of the scale in question, it's a flat 7th. When the naturally occurring 7th note of a given major scale is added to that scale's triad you will have created a "Major 7th" chord. When the music just calls for a 7 chord, without adding the word "Major", as in G7 or C7, this means you should add a flat 7th to the chord, this being a note which doesn't even appear in the scale. Where the actual 7th note of the scale is to be added to the chord, it will be specified as in, for example, Gmaj7 (GM7) or C maj7 (CM7).
So the number system just follows the numbers of the scale of the key you're in, letting each note represent a major chord (which has the same name as the note) excepting only the 7 chord, where a "7 chord" is based on the flat seventh note of the scale associated with whatever key the piece is in.