The best diagram for explaining a free market that I have seen is the circular flow diagram. There are examples of this diagram in each of the links below.
The circular flow diagram represents the ways in which resources flow within a free market. It shows that consumers spend money buying things from firms. At the same time, firms are buying labor from consumers. This is a representation of a free market because it shows that businesses will decide what to produce based on what consumers want. The idea that it is consumer demand that decides this is the basis of a free market economy.