common descent (shared ancestors) and selection on randomly occuring heritable variation in a population leads to diversity of organisms.
support for common descent of all life: DNA as molecule of heredity, relationship between transcription (DNA to RNA) and translation (RNA to protein) in all cells, adenosine triphosphate (ATP) as "energy currency" of all cells, and Phospholipd bilayer cell membrane used by all cells in different variations. all cells have shared chemical characteristics.
if something was found that didn't have a phospholipd bilayer and something else would falsify the idea of common descent.
Heritable selection: DNA is the molecule of inheritance in all living organisms and changes to DNA can happen by chance when DNA is being copied (mutation). artificial selection of dogs is used to pick certain characteristics and passed on to descendants.