On your league home page click on the "Trophies" tab; this takes you into your league's trophy catalog page with all of them displayed prominently for everyone to see. If you're the commish click on the "Trophy Catalog" page - there you'll find a link to create and assign new trophies. You can then click on the "Create a Trophy Now" to access all the options, including the type of trophy, the artwork, naming your new masterpiece, writing the description and assigning it a star value. The number of stars (1-5) indicates the "value" of the trophy - the more stars, the higher the value. And of course if you'd like to have a "trophy of shame" for let's say the lowest score of the week we offer negative values as well - I'm sure all of the bottom dwellers in your league will be thrilled to receive that one!
As the season plays out you'll start racking up the stars from your trophies, creating a second set of standings within your league displayed on the "Trophy Leaders" page. The commish can also create automatically assigned trophies that will be awarded to the owner who meets that trophies' requirements. They may (and probably will) change hands throughout the season.