Try to narrow to a period in time, to a style, and then to an artist.
Can you identify the style?
Think about the tools, supplies, and skills available at different times
Are there clues in the content of the work (the people, buildings, etc.)?
Think about the evolution of an artist's work to date it
You'll get better at this the more you study art history, but remember that you have an instinct for it as well. Even honeybees can differentiate between Monet and Picasso paintings! Play art history quiz games online or on your phone to practice identification: