I find with my new students, and even some of my peers, that often times they aren't up to par on knowing where they are in a progression while improvising or if in fact they know what chord is being played are unable to choose which notes fit the chord. Try holding an F against a C major chord...it sounds almost out of tune, like you either need to have the chord change or the F has to go somewhere for it to sound resolved.
 
Enter the Circle of 5th's. This tool is the beginning of understanding and memorizing which notes belong in what keys. We're talking about a finite group of pitches here [western music is really just twelve notes before they start repeating] so we're naturally going to have some similarities. Once you know what notes are in a key you can start to figure out what the chord set is going to be for that key. I won't get too deep into this now but check out this example.

The Key of C has these pitches
 
C D E F G A B C
 
So once we have this, you can start to build chords by taking this relationship...
 
Root (or 1), 3rd, and 5th of the scale and combine those notes wherever you want on the fingerboard or keyboard. So a C major chord will be
 
C E G
 
More on this later... Here's the Circle of 5th's and how to use it below

The key of C major at the top of the circle is where we begin to understand the Circle of Death...I mean Fifths. C major has all natural tones in it, no sharps no flats, just the white keys on the piano, however you want to think of it. That's what the Zero above the C means. Again, Zero Sharps and just as many Flats.
 
As you work your way around to the right you'll see each key has one more sharp than the one before it.In the key of G, there is the number ONE written next to it. This tells us there is ONE sharp in this key. To find out which note is raised or sharped you go the list called 'Order of Sharps' and go the first letter in the list. You should find 'F'. In the key of G, F is sharped (the key consists of these notes G A B C D E F# & G). Let's do another example. The key of A has THREE written next to it. This key has THREE sharps in it. to find out what they are, take the first THREE notes in the Order of Sharps and this will tell which notes are raised. With any luck you would have found F,C & G.
 
All of the keys to the left of C major work the same way, you would just use the 'Order of Flats' to find which notes have been lowered. The key of F major has a ONE next to it. Go to the Order of Flats and take the first note in the series. Found B? So in the key of F, there will just one flat, and it's Bb. Just one more. In the key of Ab now, ask yourself what number is next to the key, then take that number down to the Order of Flats and take the same number of letters from the beginning of the list. Ab has FOUR flats and they are Bb, Eb, Ab & Db. He-haw!
 
For guitarist, memorizing this is easy! Take C on the A string. Play a typical 5th [or power] chord. The second note in that power chord is G, which happens to be the next key to the right of C on the circle. Each key is a fifth higher than the one that precedes it. The order of flats and sharps is reciprocal. I memorized the order of flats first which is basically the word BEAD, then Greatest Common Factor. BEADGCF. The order of sharps is that same order of notes just backwards.
 
So the lowercase letters on the inside of the circle you ask? These are the parallel minors of the major keys we just spoke of. In the key of 'a minor' there are zero flats and zero sharps. Basically, it works out so the Major key and it's parallel minor key share the same number of sharps or flats depending on what key you're talking about.
 
I'll get to the difference between major and minor, whether parallel or relative, later on.