The process of making an anime is a complex one, with many steps and stages. This chart from AIC’s English website is a good visual overview for what I’ll be discussing:
Example storyboards from To Aru Kagaku no Railgun. Anime storyboards have 5 columns. From left to right: the cut number, the layout, the action, the dialogue, and finally, the running time (in time and frames). The layouts are only drawn roughly, because they are handled by other artists in the next step of production.