That effect is done with a "curves" adjustment. Select the portion of the image you want to modify (for example with the rectangular selection tool) then either create a curves adjustment layer (photoshop) or select Filter -> adjust colors -> curves (Fireworks).
On the Curves graph you'll see a straight line with a point in the lower left and one in the upper right. Click and drag the point in the upper right straight down to darken or drag the point in the lower left up to lighten the selection.
This is also useful if you want to put text over an image because it reduces the contrast too, making the text easier to read (reducing the transparency doesn't reduce the image contrast).
Before you start adjusting the curves, you should draw your grid - use the line tool and rulers/grid and "snap to" options to get the boxes even.
Hope this helps - sorry but I'm on my way out and don't have time to describe it in more detail right now...
