The Short Version

Using barre chords, you can easily play any guitar chord just by memorizing a small number of them. With the barre chord, you simply mimick a chord higher up the neck by using your index finger as the nut by barring all the strings. Most commonly this is done with the E and A chords:

 E     A
-0-   -0-
-0-   -2-
-1-   -2-
-2-   -2-
-2-   -0-
-0-   -X-

By using your index finger as the nut, you can make this shape with your other fingers and basically shift the key up. For example, if you shift E up one, you get an F which looks like:

-1-
-1-
-2-
-3-
-3-
-1-

You can keep moving this up the fretboard, and the chord you get is whatever the bass note is (i.e. the note on the first string for an E shaped barre chord, or the second string for an A shaped barre chord). So, in order to play the chords, you'll need to know the notes of the first two strings, so let's just review (you do know the chromatic scale, don't you?) up to the 12th fret (they just repeat, and remember that a sharp is the same as a flat for the next note, i.e. A# - Bb).

A  A#  B   C  C#  D  D#  E  F  F#  G  G#  A
E  F   F#  G  G#  A  A#  B  C  C#  D  D#  E
0  1   2   3  4   5  6   7  8  9  10  11  12

Now comes the fun part. With the above information, you can play any major chord. But there's a lot more chords out there than that! So as an easy reference, I'll show some of the basic shapes for some of the more popular chords. These are just the shapes of the E and A chords, but I'll show them as F and Bb chords which are the first barre chord on the neck.

E Shaped Chords

 F    F7    Fm    Fm7   Fmaj7  Fsus4  F7sus4
-1-   -1-   -1-   -1-    -1-    -1-    -1-
-1-   -4-   -1-   -4-    -1-    -1-    -1-
-2-   -2-   -1-   -1-    -2-    -3-    -3-
-3-   -3-   -3-   -3-    -2-    -3-    -1-
-3-   -3-   -3-   -3-    -3-    -3-    -3-
-1-   -1-   -1-   -1-    -1-    -1-    -1-

A Shaped Chords

Bb    Bb7   Bm    Bm7   Bmaj7  Bsus4  B7sus4
-1-   -1-   -1-   -4-    -1-    -1-    -4-
-3-   -3-   -2-   -2-    -3-    -4-    -4-
-3-   -1-   -3-   -1-    -2-    -3-    -1-
-3-   -3-   -3-   -3-    -3-    -3-    -3-
-1-   -1-   -1-   -1-    -1-    -1-    -1-
-X-   -X-   -X-   -X-    -X-    -X-    -X-

Now, these are by no means all the chord shapes, but they are the most common ones. For the rest, you can get the shapes from The Everything Guide to Guitar Chords. Armed with this knowledge, you can now play any guitar chord your heart desires! As an added bonus, because the shapes for these chords are all similar and you can slide up and down the neck, it makes changing chords fast and easy. Enjoy!