In my experience, IF they are properly staffed, security will notice the bottle as you go through the screening process in the terminal. They will ask you to take your bottle over to a table at the side. A person at that table will inspect the bottle and determine wether it is permitted on board and if the corkage fee applies. If it does apply, they will write up a slip of paper with your name and cabin number on it. They will put a sticker on the bottle to indicate corkage has been paid. You then proceed on to the ship with your bottle.
If the bottle is not permitted, they will likely confiscated it and you will get it back at the end of your cruise.
A day or 2 into your cruise (it has varied for us), a charge for the corkage will appear on your on-board account. It usually shows as coming from a particular bar or a specialty restaurant. So sometimes you might wonder what that charge is for. But it should match the amount of the corkage fee. They seem to process all the corkage receipts at one time in one of the bar/restaurant locations and then run the charges through that location.
IF they are NOT staffed properly at security, they may not even care to check your bottle out, in which case you just proceed onward to the ship with it. Don't bring it up if they don't.