Prior to determining the best way to study for an art appreciation course, one must understand the purpose of art appreciation. Art appreciation is not a course designed to teach one to create art, but is purposed for teaching one to appreciate that which has already been created. Various study methods are acceptable and must cater to the student's learning style.
One method of studying for an art appreciation course is utilizing the "Charlotte Mason" method. This is a hands-on method that teaches the child why the art is to be appreciated. For example, Monet loved landscapes, and he painted many of them. One could simply explore the landscape around oneself in order to gain a better understanding of the works of Monet.
For others, however, the simple and trusted method of memorizing facts through creating flash cards for vocabulary is often the most stable method of studying for an art history class. Separating the flash cards with terms and organizing the terms with regard to the appropriate period of art is one method used.
Nothing can beat using the syllabus, though. The syllabus is a great guideline for what will be covered in the course and what students will most likely be tested on. Always listen for the words from the instructor "...and this is important..." Those words are always clues for other items that may not be included in the syllabus, but that the instructor may include on the test.