In case you were watching the Angels-White Sox last night and wondered, here are the rules that apply:
Rule 6.05 (b)
A batter is out when a third strike is legally caught by the catcher; “Legally caught” means in the catcher’s glove before the ball touches the ground. …
Rule 6.09 (b)
The batter becomes a runner when the third strike called by the umpire is not caught, providing (1) first base is unoccupied, or (2) first base is occupied with two out; When a batter becomes a base runner on a third strike not caught by the catcher and starts for the dugout, or his position, and then realizes his situation and attempts then to reach first base, he is not out unless he or first base is tagged before he reaches first base. …
MLB.com has the video.