Just use divs where they are actually needed to accomplish the layout. Divitis occurs when far more divs are used than are needed.
In terms of how to construct it, it depends on what content you want in there. Your image above doesn't give an indiction of what the page contains, other than boxes, which isn't a lot to go on. But I guess, as a general guideline, you'd start a layout like that with a wrapper div that contains three full width divs, one atop the other. In other words, you start your inner structure with three rows of divs.