This blog is not a "how to" guide for technical questions. There are so many great books available it would be pretentious of me to assume that I have any different technical wisdom to offer but two things you might try on a grey day is a long exposure (with a tripod of course) and applying an infra-red filter to a black and white image in the digital darkroom, as I did with this image. It can do some nice things with tonal ranges.
What is more important than these technical considerations this kind of day presents is the idea that merely sitting in a landscape like the one above, quietly listening to the cry of a lone gull and feeling completely detached from your "other life". It is something everyone, photographer or not, should experience. The incredible sense of peace and "other worldliness" is breathtaking. I am very fortunate to live in a state (Maine) that offers many of these fog-filled days along the coast. The air smells different on a grey day and you almost feel as if time is suspended. With no sun marking time across the heavens, it could be anytime. Timelessness is an entrancing quality and one I hope all of you get to experience.