Bidders will receive an automatic winning text message after the auction closes if enabled under Software Settings > Auction Settings > Payment. This message can be edited as you wish, and can include the [p] shortcode to bring your bidders directly to the payment screen. Here are other ways your bidders can find out if they won:
Menu > My Items: In the bidding site, bidders can look at their "My Items" page
Allow Guests to Checkout from Phone: This feature can be turned on under Software Settings > Auction Settings > Payment. When a bidder clicks the red Pay! button it will show them a list of all items they won and allow them to check out.