Bidders submit either competitive bids specifying a yield or non-competitive bids that accept whatever clears. The Treasury fills from the lowest yield upward until the size is covered; the last accepted yield is the stop-out, and everyone pays it. That single-price format stops bidders from shading their bids to avoid the winner's curse.
Traders watch three numbers: the bid-to-cover, the auction-tail, and the split between primary-dealer takedown and indirect bidders. A weak auction can move the whole curve within seconds of the 1pm result.
Example: a 10-year auction of $39 billion attracts $130 billion of bids and stops at 4.185% when when-issued was trading 4.175%. That is a 1 basis point tail and a bid-to-cover of 3.33, a mediocre but not disastrous result.
Related: bid-to-cover, auction-tail, when-issued, primary-dealer, quarterly-refunding