Freud identified the subconscious desires that motivate us; these desires are not rational but come from primitive needs. In Freud's model, the three parts of the mind are the id, from which primitive needs for revenge and murder arise; the superego, which dictates what we should do according to societal norms about what is right; and the ego, the principle of realism that mediates between the id and superego.

In this scheme, Captain Ahab clearly represents the id, as he drives his boat towards a disastrous chase of the white whale, Moby Dick, out of a desire for vengeance. The superego is perhaps best represented by the white whale itself, who punishes Ahab and defies his desire for murder and bloody gratification. Ishmael, the narrator, represents the ego, as he tries to mediate between the battle of Ahab and the whale. In the end, it is he, representing the ego, who is the sole survivor, indicating that the ego persists through the battle between the id and the superego. 

A novel as complex and multi-faceted as this one offers many different ways to apply Freudian psychoanalytical theory to the text (and many avenues for the application of other modes of critical theory). 

To take a broad approach, we might begin by trying to situate the novel in terms of the Id, Ego and Superego and identify elements of the text that match this Freudian structure.

In doing this we might identify Moby Dick as a representative of the Id. Living underwater in a metaphorical subterranean state and a literally submerged one, Moby Dick may be seen to symbolize the blind and chaotic forces of the unconscious mind. 

Captain Ahab, bent on establishing mastery over the chaotic world of the sea, may be taken to represent the Superego. While he is not "civilized" in all sense, Ahab is definitively associated with a will to control, a will to power, and a penchant for subduing any force that would contradict him. 

“There was an infinity of firmest fortitude, a determinate, unsurrenderable wilfulness, in the fixed and fearless, forward dedication of that glance.” 

The crew then would be the Ego, managing the conflict between the opposing Id and Superego. The crew is both self-representative and is symbolized (via synechdoche) by Ishmael, here the Ego par excellance, conscious and aware of a pull in sympathies going in both directions. 

We might further consider the novel in terms of wish fulfillment (as Ahab is compensating, perhaps, for a childhood deficiency or trauma in his desire to either kill Moby Dick or sink the Pequod, or both).