Yes, agreed with Eliot: "would" is not a past tense. Modals don't properly take on a tense, you normally need to conjugate other verbs around it to indicate the tense. I've read the dictionary definition which says that it is a past tense of will, and that's a pretty shoddy definition with poor examples. Don't be misled. ;)
Use would for imagined situations, such as conditionals, or to express someone's intention or wish. In your example, "I'm not sure how she'd want me to-" means the speaker is not sure as to Cuddy's(?) wishes about how she wants the situation handled.