A guitar chord chart is a picture of a section of the fretboard and neck if it was standing up vertically. The vertical lines are the strings, and the horizontal lines are the fret bars.
The vertical line furthest to the right is the 1st string, and the furthest to the left is the 6th string. If the top horizontal line is thicker, then that represents the nut of the guitar. (see parts of the guitar) Then the next lower horizontal line is the 1st fret bar, and the next lower would be the 2nd and so on.
The dots tell you where to put your fingers, and the numbers underneath the chord chart tell you what fingers to use. A 0 stands for an open string. An X means to either not play the string, or mute it. We will talk more about muting a string shortly. If there is a T, then you use your thumb to play that note.