To study lung tissue under a microscope, sections are typically obtained through a process called fixation, embedding, sectioning, and staining. Fixation with formaldehyde preserves the tissues, embedding in paraffin wax allows for thin slicing, sectioning involves cutting the tissue into thin slices using a microtome, and staining with dyes like Hematoxylin and Eosin (H&E) enhances the visibility of cellular structures.