How do offers and giveaways end on their own?

In an Offer Grid block, each offer has Starts and Ends fields (a date and time), plus Sponsor or Operator, Eligibility, and an Official Rules link. Once an offer's Ends time has passed it shows Ended in place of its entry button, so nobody can enter a finished giveaway. By default an ended offer also drops off the page. Turn on Show Ended Offers on the block to keep past offers listed with the Ended label.

Keep one Offer Grid block for a promotion and reuse it on Home and on your Offers page, so changing the end time in one place updates every page that shows it. A third-party auction is the same thing: name the operator in Sponsor or Operator and put its close time in Ends.