Mount a sample of the cell under a microscope.
Increase the magnification until the different areas of the cell, including its appendages and nucleus, are clearly visible.
Look at the overall size. Unicellular organisms are much smaller than multi-cellular organisms.
Look at the center of the cell and search for evidence of a nucleus and nuclear membrane. The membrane is a clear substance that encloses the nucleus for protection. Lack of a nucleus and/or nuclear membrane indicates that this is a unicellular prokaryote.
Look for evidence of organelles, small organ-like structures that perform dedicated functions. A lack of organelles also indicates that this is a unicellular prokaryote.
Verify that there is only one cell or that the cells visible act independently of one another. Bacteria grows in clustered colonies, but each unicellular organism acts independently of the others and is capable of surviving without the rest of the colony.