Christina Rossetti's "Goblin Market" is a wonderful poem that can be approached through a variety of critical perspectives. The wikipedia link given below briefly discusses several approaches (see the brief section on “Criticism”), For a purely psychological approach, I would recommend focusing on one of the following possible topics:
1. Addiction or other obsessive-compulsive thoughts and behaviors: The poem can be read as a fictional treatment of a very real pathology. Laura is consumed by an overwhelming desire for something, and that desire is so extreme that it wrecks her life. She is cured at the poem’s end, apparently.
2. Approved and marginalized forms of sexuality: The poem can be read as a treatment of the types of expressions of sexual desire by young women. The two sisters touch a lot throughout the poem, the goblin men are leering and animalistic, and the one approved form of sexual expression--heterosexual marriage--is brought up again and again in the poem.
As you know, a critical approach to a literary work usually balances a discussion of the theoretical model (in this case, a psychological theory or approach) with a discussion of the literary work itself. Good theorists to look at might be Freud (for discussion of infantile and adolescent sexuality), Jung (for discussions of archetypes), and perhaps more recent theorists who deal with obsession, addiction, or related topics.
I hope that these comments help you get started.