On your League Home page, the header has several links. The third link from the left is "Trophies". Clicking on that link will take you to your league's trophy page. Here you will see trophies listed in chronological order as they are assigned.
Click on "Trophy Catalog". On the Trophy Catalog page, the League Manager will also see a link to create and assign trophies.
Click on "Create a Trophy Now" to get access to trophies options. Options include, the type of trophy, the artwork, naming the trophy, writing the trophy description and assigning a star value.
The number of stars (1-5) indicates the 'value' of the trophy; the more stars the more value. Additionally, trophies with a negative value can be created. For example, some leagues will issue a mocking trophy for something like the lowest score of the week. The LM can assign a value of negative stars (minus 1-5).
Once created, the LM will have the ability to assign the trophy from the Trophy Catalog page.
Over the season, the number of stars will accumulate creating a second set of standings with the league. These standing are displayed on the "Trophy Leaders" page.