Pike takes Kirk with him off the bridge down to hangar after asking for volunteers with experience in combat (German Comment: "Sie kommen mit, Kirk, Sie gehören sowieso nicht auf das Schiff" (transl. You come along, Kirk, you don't belong on this ship anyway), to stop the drill, when Pike himself answers Neros invitation to shuttle over to Narada. On their way to Shuttle Bay (Spock's with them, arguing about something I have forgotten to quote it to the letter). Also is Sulu with them and one redshirt
Pike gives his orders, makes Kirk First Officer (means, that Kirk will be in command for this mission on and to the drilling thing ...) and leaves Spock in Command of the Enterprise "You're the Captain. ...(orders) ...".
*later*, after Kirk getting under Spocks skin, Spock leaves the bridge ... THEN McCoy makes his statement "Fantastic (ironically) now we have no Captain, and no first officer to replace him." (free fom German dubbing)
Kirk wheezes for air, after the fight, comments after a few blinks: "Yes we do ..."
McCoy about to argue "What in the hell ..."
Sulu intervenes with his thumb directed to Kirk: "Pike made him First Officer ..."
So, all is said and done, ... by the book. *nerd, nerd*