Explore the various "levels of the mind" as they relate to characters or mass psychology in the literature. Freud separated the mind's force into a trinity: id, ego and superego. The way characters use these three mental powers to navigate life's events is central to a Freudian analysis.
Look at the "mental energy" of a character. Freud used the word "libido" in a general sense to illustrate use of mental energy. We tend to use libido and it's inherent "mojo" as a sexual references, but that's not the only application of the term.
Look at the way characters handle or express repression. Repression is a theme in Freudian work as a necessary aspect of psychology mediating action.
Examine psychic conflicts in the literature. If a character grapples with himself it can represent a conflict between two "Freudian entities" and can be analyzed as such.
Examine any instances of "hypnotism" in the literature. Freud dealt widely with these overt manipulations of the mind, and any reference to hypnotism is a good subject for Freudian critique.