When he was still going by the name of Leroy Jones, Amiri Baraka wrote a play that was made into a film called The Dutchman.
In it you can see, painfully and clearly, the intent of the writer's work - to display the insanity, degradation, and blindness that characterized race relations in the United States mid-century. Sociological Criticism will contextualize Baraka's work, examining 1) the social and political atmosphere that helped to create it and 2) accounting for stylistic, metaphoric, and technical elements of the work which can be related to sociology, or the study of different peoples.
I'd encourage you to check out an overview of Sociological Criticism first. Any writing you would want to do relating Baraka to this vein of criticism should be fairly straight-forward after that.
Sociological literary Criticism is criticism of literature in light of the work's sociological context. Marxist Criticism is a form of Sociological Literary Criticism. Kenneth Burke is credited with developing the concept through his article "Literature as Equipment for Living". If you read the e-notes article about him, you'll find information on his "pentad" for dramatic analysis that should help you with Baraka's plays. Certainly Burke's approach (seeing literature as something that makes things happen) would fit Baraka's dramatic purpose which was to challenge society's beliefs through protest.