I employ grid drawing from time to time, but was frustrated by portions of my drawing that got erased with the lines of the grid, coupled with the "ghost lines" that would appear when I chose to color the picture I just drew. So, I took a piece of cardstock, and drew the grid lines on it, using a dark pen. The gridded cardstock can be readily seen through most types of white drawing paper, and the time formerly spent on erasing is now freed up.
To add to SilverGriffin's great tip - if you are using heavier drawing paper, you could draw your grid on paper, and use a lightbox (or a window on a sunny day) so that you can see the lines through the paper.
