I understand I need to pick up a Mythos card during the Keeper's turn, but when do I pick up and use Trauma cards?
The rules on Trauma cards are on pg25 of the Rules of Play book.
These cards can only be played by the keeper immediately after an investigator takes damage or horror. The only exception to this restriction is if an investigator has zero sanity, in which case the keeper may play one insanity Trauma card on the investigator as a keeper action (once per turn per insane investigator).
The main way to get Trauma cards is to use Keeper actions, particularly the Evil Presence and Dark Ritual actions. (All 5 stories in the base game have one or the other available to the Keeper)