The cylindrical shell method is a technique used to find the volume of solids of revolution by integrating the lateral surface area of cylindrical shells. To derive the general formula for the volume of a sphere and a cone using this method, one must set up the appropriate integral based on the axis of rotation and the shape's dimensions. The discussion highlights a need for clearer explanations and resources, as the provided link to a lecture is currently unavailable. Users express frustration with insufficient textbook guidance on this topic. Understanding the cylindrical shell method is crucial for accurately calculating volumes of various geometric shapes.