I love this design for its arresting weirdness but I'd be the first to admit it's terribly impractical, confusing, and bulky (compared to the final version).
It works through diagonals. Say you want to find out what day February 2 falls on. First, find the number. Then, move through its diagonal (the 2nd diagonal left-to-right in this case, the white one) until you cross February's row (FEB). At the cell where they cross (the one with a 16 in this case), go up to find the dayname--"MIE", which means February 2, 2007 falls on a Wednesday (MIErcoles).
It is not that complicated--slide through the diagonal until you cross the month row, up from there--but there's a lot of contradictory information along the way.