While an auction is still live, access your "Following" (this list can be found at the top navigation bar of any page) and view your list of items that you are following as well as bidding on. (If you bid on an item, you will be automatically "Follow" that item). If there is a green trophy to the right of an item, you are currently winning! If there is a red circle with a line through it, then you were outbid.
If you are watching an item close, make sure to refresh the page frequently within the last few minutes, as some internet connections can time out during the last few minutes of an auction. Don't worry! The auction will extend for 5 more minutes if you are outbid. Make sure to edit your auto-bid in order to make sure you are not outbid!
The closing time on each item in a sale is staggered; after you win your invoice will be emailed to you and available to view under your "Won Items" approximately two hours after a sale closes.