Swedish Naturalist Carolus Linnaeus devised a system of grouping organisms into hierarchical categories according to their form and structure. Aristotle classified organisms into only two taxa - either plants or animals.
Scientists examine the creatures cell structure to see if it is prokaryotic or eukaryotic. Prokaryotic organisms are usually simple organisms and eukaryotic ones are complex. For example, humans are eukaryotic. Bacteria is prokaryotic.
Aristotle initially divided living organisms only into two groups which are plants and animals. The system was not proven to be good because there were too many species of plants and animals. However, the system was used for 2000 until the time of Linnaeus.
By single organisms I assume you mean unicellular organisms. That is one of the more well accepted theories involving the origin of multicellular organisms. It is, however, far being definitively proven.