I'm not sure how she'd want = she would want It's not really a tense. It is a modal auxiliary. "Would" is used in conditional statements. (If I asked her), what would she want me to do? I'm not sure how she'd want me to --- (the sentence is interrupted here!) Hold on a minute - comes after the interruption!

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.

would is the past of will we use would to express wish, desire, request and others. she said she 'd meet us at the store. would you make me a cup of tea, please? i wish you would stay. if i had money, i'd buy a car.(possibility) jane said she would come with us.(here it indicates uncertainty)