Major Chords

C:

EADGBE
x32010

G:

EADGBE
320003
or 
EADGBE
320033

E:

EADGBE
022100

A:

EADGBE
x02220

Minor Chords

Dm:

EADGBE
xx0231

Am:

EADGBE
x02210

Em:

EADGBE
022000

Seventh Chords

A7:

EADGBE
x02020

D7:

EADGBE
x00212

E7:

EADGBE
020100

C7:

EADGBE
x32310

G7:

EADGBE
320001

B7:

EADGBE
x21202

Barre Chords

These are made by "barring" across several strings with the index finger.
Notice that an F is just an E up one fret. Same with A to Bb.

These are much harder! Master the others first.

F:

EADGBE
133211

Bb:

EADGBE
x13331