The grid on the left represents one of two things. If you are displaying an open chord, it shows the first three frets at the top of the neck. If you are displaying a moveable chord, it shows four frets, including the one with the bar and the next three up. To find out which fret the bar should be at for the chord you want, see the table of barre chords.

If a string has an 'x' above the nut or level with the barre, avoid playing it, preferably by carefully muting it with a finger or your thumb. (If you find that this makes a quiet ringing noise when the string is struck, move the finger up or down the string). If there is an 'o' above the nut, the string should be played, but not fretted. If a string has a solid circle placed over it at a particular fret, fret it there. If the circle has a dashed edge, the fretting is optional, but in general, if a chord has two optional fingers, either fret both or fret neither.

My notation as regards chord names has undergone efforts to standardise it, and a full table of names, pronunciations and equivalents that you might see elsewhere is here.