Restaurant or Bar Owners. If you offer a free drink or meal to a customer should you pay?

I'm pretty new to the restaurant and bar business and would like to know whether manager's or staff members who offer a complimentary drink, meal or dessert should A)just keep a receipt to explain the short on the register B) Not ring it up on the register at all C) Have every item regardless of the promotion (free drink to best dressed ladies or one drink to a very loyal customer) Paid for from the bar's sales, manager or staff members income or the business's account. And then what should it go under in terms of accounting?