Why are players thrown out of a face-off? I've heard there is a certain procedure for these circumstances, but I haven't found a list of things that are considered 'illegal'.
As stated in the Official NHL (National Hockey League) Rulebook in rule 76.6, players must comply by the following standards, otherwise it will result in a face-off violation:
i) Encroachment by any player other than the center into the face-off area prior to the puck being dropped.
ii) Encroachment by any player into the area between the hash marks on the outer edges of the face-off circle prior to the puck being dropped. Players must also ensure that both of their skates do not cross their respective hash marks.
iii) Any physical contact with an opponent prior to the puck being dropped.
iv) Failure by either center taking the face-off to properly position himself behind the restraining lines or place his stick on the ice (as outlined in Rule 76.4).
v) The blade of the stick must then be placed on the ice (at least the toe of the blade of the stick) within the designated face-off area.
Violation of these rules will result in removal from the face-off (the center) and normally one of the wingers comes in to take the re-drop.
Any 2 face-off violations committed by the same team during the same face-off will result in a Delay of Game minor penalty for 2 minutes.
Included is also a link to the Official Rulebook for further reading and long form rules: http://www.nhl.com/nhl/en/v3/ext/pdfs/2012-13_RuleBook.pdf