NHL Official Rules (PDF)
Outside of the entirety of playoff overtime hockey, I honestly find an in-game penalty shot to be the most exciting event in hockey to witness. These rules also apply to shootout shots.
Rule 24 - Penalty Shot
24.1 Penalty Shot: A penalty shot is an even-up situation where a scoring chance on a breakaway is restored after a foul from behind (or some other infraction that triggers a penalty shot).
24.2 Procedure: After a team's been awarded a penalty shot, the puck will be placed at center ice. On the referee's whistle, the player taking the shot will take the puck and take . . . well, a shot (it's called a penalty "shot" after all) on the goalie.
"The puck must be kept in motion towards the opponent's goal line," not necessarily just the net. Goal line extended is still the goal line, so it is still legal for a player to take the puck way wide to the side on a penalty shot. Personally, I also like the idea of a player being mandated to keep the puck going toward the goal because it removes the needless crap of a player deciding to twirl around before taking the shot; it prevents wasted time. It also evens up what would be a huge advantage to the skater if the skater were allowed to constantly move side to side and back and forth until he saw an opening he liked because the goalie is just exhausted.
". . . once it is shot, the play shall be considered complete." The play ends when the puck crosses the goal line (either inside or wide of the net) or when the puck is propelled away from the goal line or comes to a complete stop, either by a goalie save, by a pokecheck, or by a shot hitting the post. The only kind of "rebound" goal allowed on a penalty shot isn't really a rebound at all, just a bunch of deflections: goal post or crossbar, off the goalie and directly in. Once a player has shot the puck, he's not allowed to get another touch on it.
There's no actual definition of what constitutes a "shot" here. I guess they defer to the porn definition: you know it when you see it. Granted, it is difficult to come up with an airtight definition of what would constitute a shot that would result in the penalty shot being completed. A quick glance at the rest of the rulebook doesn't produce any other section where "shot" is defined. At least if they did find a way to define it, it might help eliminate home arena scorer bias.
Players are allowed to pick the puck up and handle and shoot it like a lacrosse player so long as the puck is never raised above shoulder-height while handling and not above crossbar-height on the actual shot.
The spin-o-rama (hereafter "spinorama") is still legal in the NHL, despite conversations about removing it from the shootout, and by extension any penalty shot; as an aside, it's banned by the IIHF. The justification for not banning it in the NHL is that the spinorama involves continuous motion, which supposedly doesn't violate the spirit of keeping the puck in motion toward the goal. The rulebook does explicitly state that "should the puck come to a complete stop at any time during the shot attempt, the shot shall be stopped and no goal will be the result."
Only goalies, not skaters, are allowed to defend against the penalty shot. I have to think the NHL doesn't want skater vs. skater 1-on-1 with an empty net, so they decided to spell it out explicitly that only goalies can defend against a penalty shot. I honestly think it'd be amusing to see at least once, but I'd get tired of it pretty quickly.
Speaking of goalies, they have rules to follow too: he has to stay in the crease until the player taking the shot touches the puck. If he's allowed to wander before the player touches the puck, then it becomes a similar issue with a skater attempting to defend a penalty shot: it's not so much protecting against a "shot" as much as trying to just poke the puck off the skater's stick.
The next paragraph confuses me:
If at the time a penalty shot is awarded, the goalkeeper of the penalized team has been removed from the ice to substitute another player, the goalkeeper shall be permitted to return to the ice before the penalty shot is taken.
We'll get to "Awarded Goals" in Rule 25, but suffice it to say that for every scenario I can imagine where a team removes its goalie for an extra attacker and subsequently commits a foul that would result in a penalty shot under normal circumstances, the end result is an awarded goal to the non-offending team. In other words, if the Red Wings have pulled Jimmy Howard for an extra attacker and then Niklas Kronwall commits a foul that would result in a penalty shot, it just becomes a goal against rather than a player taking a penalty shot against an empty net. (Although history tells us even that's not a surefire goal.) So what is this about "the goalkeeper shall be permitted to return to the ice before the penalty shot is taken"?
The next paragraph is also confusing:
The team against whom the penalty shot has been assessed may replace their goalkeeper to defend against the penalty shot, however, the substitute goalkeeper is required to remain in the game until the next stoppage of play.
First, I think we can all understand that the goalie who defends the penalty shot has to stay in net until the first stoppage of play after the penalty shot attempt. (Although it doesn't clarify if the goalie has to stay if that stoppage of play is an icing.) But the confusion for me arises with the inconsistency of using "replace" and "substitute." It's written as two separate paragraphs, but does this paragraph follow from the previous paragraph about a goalie being permitted to return to the ice if he was pulled? And why does it say "may replace their goalkeeper" instead of "may substitute their goalkeeper"? Does that mean that if, for whatever reason, we wanted Jonas Gustavsson instead of Howard to defend against a penalty shot, tough luck, that's against the rules? Or are we actually allowed to switch goalies for a penalty shot?
While the penalty shot is in progress, all players that were on the ice are to withdraw to the area directly in front of their own benches (except, of course, the skater taking the shot and the goalie defending against it).
We're over a thousand words in and there are still six other subsections to cover, a couple of which are quite lengthy. We'll be talking about penalty shots for at least another post or two.