I have seen them in many sizes and levels of completion, from scribbles on a napkin to animatics with actual CGI and motion in them, and I have seen boards in tiny boxes running down a third column of a 2-column script, to poster-board size with from three to nine to 20 frames on them, with and without captions under. You didn't say if this was for a movie, a music video, an effects sequernce, a TV spot, or what.
So I'd say I'd be surprised to know of a "standard", though if I was going to use them myself, I'd tend to go with the posterboard size with six to nine individual frames about the size of my hand, and up to 3 lines of captioning under each of the frames, which is what we used to use when composing 30-second TV ad pitches in school. At work I used 8&1/2 by 11 inch standard pages with a 3-column arrangement (Picture, audio, video description) or 2-column (Pics downthe left, copy down the right). If you're doing something longer and more elaborate, you'll have more frames to show, obviously, and then the individual frame sizes will have to get smaller to fit on one or two boards. Or you get way more boards:-)
Premade storyboard tablets are available thru better art supply stores and places like Markertek.