Though storyboards are beneficial in animation, many do not use them as often for Brickfilms. Brickfilms are shorter, and therefore do not take as much planning. Also, the person who creates the script/story is, more often than not, the one capturing the images. Still, storyboarding can be helpful for planning how to set up your scene as well as set up desired camera angles.
Storyboards can be as simple or complex as you desire. Since most want to get right down to the animation, stick figures work just fine. Also, include the audio that will be in the scene. This includes dialogue, sound effects, and background. It is helpful to write out how many seconds each scene will be so that you know how long you need to animate the characters.