Get a decent graphics program (Paint Shop Pro, Adobe Photoshop, etc -- anything that supports "pattern fill" and layers) and draw a grid pattern with the line tool. Now make a new image of the same dimensions as the final map and use the "pattern fill" on that. If you drew the grid right (you should be sentient enough to figure that out by yourself), the patttern lines up correctly and you got a large grid.
Now open the map and add the large pattern filled image you created as a new layer on top of the map, set the opacity to a low level or use the "overlay" rendering (depening on whether you used a black background for the pattern or a transparent one), e voila.
If you didn't understand that, google for a tutorial on layers or patterns.