To simplify, there are two ways to interpret art. The first is the easiest, involving only the artwork and its audience, with no outside interference needed. Many schools of thought consider this the only way art is really interpreted. This basically boils down to a series of Socratic questions: How does the artwork make you feel? Why? And, to a lesser degree: What do you think the artist was trying to evoke/say/communicate with the artwork?
This first method requires little to no preparation and is as much about the audience as it is about the artist and his/her work. Still, this doesn't mean that this is the "lesser" form of interpretation. In actuality this is the purest form that art interpretation can take, and does not even have to be passive. A reaction to an artwork can be a piece of art in reply, or even just a little bit of impromptu self-discovery.
The second method involves more of the artist and the time period. This is, of course, the better-known methods to fellow students of art appreciation class. This entails taking into the account the artist and the historical and artistic time period of both the artist and, if appropriate, the subject matter.
An example of this involves the symbols used in paintings. A dog or a white lily, for example, can mean different things in a Renaissance painting than it would in a modernist painting. In some cases an subject can be imbued with meaning, while in another time period the emphasis was art for art's sake, meaning the white lily is, simply, just a flower that happened to be there, rather than a depiction of feminine purity.
This method requires more research in the scholarly sense, and in some ways can be seen as an obstacle between the viewer and the artwork. In other ways, though, this method brings greater depth and understanding to a subject and its artist.