the six lines represent the six strings and the numbers on the lines are the fret u are suposed to press down.
the top string in the tab is the high e string and the bottom is the low e string.
in your example u play the opens string on the d string and the 3 fret of the b string. then u play the second fret of the b string, then u play the second fret of the high e string.
as u say this is a d chord but the notes picked out individually u will notice all the notes in that tab make the open d chord shape.
tabs fault is it doesnt tell u anything about the rythm, u ave to do that by ear.
anyway hope this is helpfull, if it was please give me rep points buy clickin the scale at the top of my message next to my name and such. plzzzzzz. i really want rep points. :D