The most important open chords are the major C, A, G, E, and D chords. For convenience, you can remember these chords as the word "CAGED". Lets look at them one by one.
* Black circles represent where your fingers go, with the number corresponding to the finger you use to press down behind the fret (1=index). The x's and open circles above the fretboard tell you whether the strings that aren't pressed down are allowed to ring or not (x= no, open circle= yes)
You will probably find that the E and A chords are the easiest to form, while the C and G are a little harder. For some, the D will be a little harder than the rest. Remember to keep your fingers curved. You want only the tip of the finger pressing down on the strings. At this point, you will probably want to curl your thumb around the top of the guitar neck, sort of like the way you would hold a baseball bat.
When you can form all of these chords, try switching between them. This is the skill that will allow you to play your first song. If you find one chord particularly frustrating, leave it alone for awhile. Go ahead and try to switch between the chords that you can play. You can always come back to what you find difficult.
Challenge Exercises
If you can play all of the CAGED chords, try this F chord out. It is sort of notorious amongst guitar learners. You have to fret the 1st and 2nd strings with one finger (1st finger). Try using the palm of your hand for support.
Here is a list of the chords that "sound good" together. This means that they are part of the same key, and are often included together in songs. Try practicing chord switching using these chords.
Key of C
C, F, G
Key of A
A, D, E *add C chord for a bluesier sound
Key of G
G, C, D
Key of E
E, A, B *add G chord for a bluesier sound
*See lesson 3 for B chord
Key of D
D, G, A *add E chord for bluesier sound