Here's a few quick methods for producing fast and dirty storyboards.
1. Keep the area you have to draw small. It allows you to draw much faster. The pictures become more like doodles than works of art. Remember the point is to get an idea of how things will look on screen. Ridley Scott (Blade Runner, Thelma and Louise) is famous for his Ridleygrams - rough, almost indecipherable sketches that outline what he has in mind.
2. Copy up a set of storyboard sheets so you don't have to spend all night drawing screen boxes. Download a storyboard sheet.
-Storyboard template 1
-Storyboard template 2
3. Sketch in pencil so you can make changes easily, then ink in for photocopying. Feel free to use any medium you are happy with - professional storyboard artists use everything from magic markers to charcoal.
4. Scribble down short notes about what's happening in shot (e.g.. BOB enters) what characters are saying ("Is this it? Is this how...") or sound effects (Roll of THUNDER).
5. An overhead plan view of the location of the camera, actors and light can be helpful if you know the location you are going to be working on.
6. Number your shots so that they can be quickly referred to on the shot list and during editing.