Names are minted via auction. All you have to do to start the minting process is place the first bid with Handshake coins (HNS). You can participate in any Handshake auction that hasn't closed yet.
Bids can take on any value and you can optionally add a blind to your bid to hide the true value of your bid from others.
Your bid blind is called your lockup, which is the only number other bidders (and the rest of the network) can see. Your HNS lockup will be nontransferable for the duration of the auction, though your blind will always be returned to you once your bid has been revealed.
After the first bid is placed, bidding is open to everyone for 720 blocks (5 days).
Everyone will have 1440 blocks (10 days) to reveal their bid price - Namebase does this automatically for you so if you're a Namebase user you won't need to worry about this step :)
The highest bid (not highest lockup) will win the name. The winning bid is chosen after the 10 day reveal period and the winner pays the second highest bid amount while the other bidders get their coins back.
It's important to note. The winner's payment is burned by the network, so the winner doesn't pay bids to anyone per se.
The end of the auction signifies that the name has been minted and the winner gets to use their new Handshake name however they wish (Namebase helps you manage its settings without being a programmer). The rest of the bidders can continue trying their luck on other Handshake names!