Pierre-Auguste Renoir was a French artist who lived from the mid-19th century through to the early 20th century. He is credited with, and most widely known for, helping to create the impressionist style of painting even though many of his later works were in a different style.
Look at the use of color. Renoir would paint in classical impressionist style. His colors would blend together without any harsh edges or strong shades. He would rarely use black; shadows are simply a darker color of the object that they originate from.
Examine his subject mater. Renoir, like many impressionists, painted subjects outside, often with emphasis on the surroundings instead of the people. The subjects of his paintings are typically going about mundane activities and are often depicted as unaware they're being painted.
Check for strong signs of classical influences hallmarking the Ingres Period. Renoir broke with some of the impressionist values in his later years as his work took on a very classical overtone. He often painted figures with much more detailed outlines and used darker colors.
Look for a mixture of styles and content during his later years. Renoir was able to do something with his later works that cemented him as a true master. He combined the severe realism of classical painting with the insubstantiality of impressionist painting. Often he manages to mix aspects of the two styles so keenly that they become nearly indistinguishable from one another.
Observe the painting's subjects. Renoir's later period had two very common themes throughout; nudes and domestic activity. Renoir's nudes are typically female and are often quite rubenesque. The other common theme, domestic activity, will often show one or more young women doing something around the house such as playing a piano or taking a bath.