There are generally two types of lighting that can be used for microscopes: transmitted and reflected illumination.
With transmitted lighting, light shines from behind an object (usually a transparent target) to illuminate the features within that target, while reflected light is used to illuminate the surface of an object. Reflected light can be coaxial (brightfield) or from an angle (darkfield). Coaxial lighting travels along the same direction as the optical path of the lens and is used to view flat surfaces. Lateral illumination reflects off of the angled surfaces of an object and is usually used for imaging objects with textured or irregular surfaces.