What three factors affect how well a person is able to view specimens through a microscope

Illumination -

An essential factor in producing a good image with the light microscope is obtaining adequate levels of light in the specimen, or object plane. It is not only necessary to obtain bright light around the object, but for optimal imaging, the light should be uniform across the field of view. 

 Magnification and Imaging -

Most microscopes in current use are known as compound microscopes, where a magnified image of an object is produced by the objective lens, and this image is magnified by a second lens system (the ocular or eyepiece) for viewing. Thus, final magnification of the microscope is dependent on the magnifying power of the objective times the magnifying power of the ocular. 

 Resolution -

The magnification of small things is a necessary facet of biological research, but the fine detail in cells and in subcellular components requires that any imaging system be capable of providing spatial information across small distances. Resolution is defined as the ability to distinguish two very small and closely-spaced objects as separate entities.