Danforth
Danforth is the Deputy Governor of Massachusetts, who presides over the Witch Trials. Miller has admitted to modeling this character after Senator McCarthy. Look for these traits. Find his motivation.

Most of your information will come from a close reading of the actual play. Pay close attention to the court scenes in Acts 3 and 4.
You might also want to check out the following books:
Bloom,
Harold. Bloom's Reviews: Arthur Miller's The Crucible.
New York: Chelsea House Publishing, 1998.
Johnson,
Claudia Durst, and Vernon E. Johnson. Understanding The Crucible.
New York: Greenwood Publishing, 1998
Martine,
James J. The Crucible: Politics, Property, and Pretense.
New York: Twayne Publishers, 1993.