ABSWER 1: Remember, there's a lot of downtime that transpires. Not just during adventures when characters are either forced to wait for something or have to travel from place to place (by conventional means), there's downtime in between adventures as well. It's not like in the old days when a subject like regeneration only came up when someone underwent one. In the new series the Doctor is a lot more sharing and a lot less cryptic (when necessary). Example: In 'the Doctor's Wife' episode, for the purposes of expediting the story it was revealed that the Doctor had already told Amy of what he had to do to the rest of the Time Lords. This conversation most likely transpired right after "The Beast Below" in which Amy learns for the first time that not only is the Doctor a member of an alien species but that he is the last of his species. Naturally the question 'What happened to the rest of your people?' would be foremost on one's mind to ask at some point upon finding something like that out. So we can assume that either before or definitely after "The Impossible Astronaut" that regeneration was explained to Amy and Rory.
ANSWER 2: Presumably, it was explained to her off-screen. We never heard the Doctor tell her that he finished off the Time Lords himself in any episodes, yet she knew all about that in "the Doctor's Wife". It's possible that she was also familiar with the nature of the regeneration process (she was shocked, but not surprised, when the Doctor began to regenerate in "The Impossible Astronaut"). It just didn't happen on-screen. I mean, the viewers know about those things already, why should we always listen to the same explanation over and over again, whenever a new companion comes along? off camera talks and unseen adventers..what theb .