How should one access HQ cards with the "Legwork"
You access the cards one at a time, but they don't go back to HQ until you're done.

Essentially, you draw one from HQ, decide what to do with it (if anything), then set it aside as you draw the next card. Once you're finished, the cards go back to HQ (unless they don't for whatever reason).

From the FAQ, page 3:


  When the Runner accesses multiple cards from HQ, the cards are accessed one at a time, and do not return to HQ until the Runner is finished accessing.


If you want to trash the cards, you must do so as you access them one at a time, not after you've accessed additional cards.