It's simple. [And Arthur's not going to tell you the whole truth unless he trusts you.] She's administered the sedative and enters into a state of dreaming. I guide her through a scenario that's been designed to help trigger the memories. [He turns to look at Capa, his expression betraying nothing.] You know, "you see a building, go into it," that kind of thing. Her subconscious supplies the rest. The drug should help her achieve greater recall upon waking up.

[This is pretty much the truth-- the only thing Arthur's leaving out is "and I go into the dream with her," because he doesn't know if he can trust Capa not to tell her, and the second Hayley knows, this thing's pretty much blown. She would be too guarded if she knew the reality of extraction.]