The short version is that everyone present for the kill gets a loot box containing a weapon. You can either pay money to ensure that the weapon is right for your class, or you can buy an ordinary key and take your chances. Once you've gotten the right weapon (with the right stats) after however many trips, you can start leveling it up... but in order to really advance it, you'll need to get two more weapons and level those up. Take a look at the full preview for details on boss mechanics and the weapon upgrade process.
[Thanks to Steparu for the tip!]