To start a Round in the Congress application, move to the third tab on the left-side navigation bar and just follow the steps on the page.
Once a Round is active, all the articles saved to bills which have been added to it will be available..
However, you can also add new articles (which are saved to your Library, but not yet to Congress) from the Smart Search feature.
When you run a search and go to the results page, while a Round is active, you will notice a '+' sign next to each article. Clicking it will open a drop-down menu with the bills which are part of the active round. Selecting the bills will save the article to it either permanently (if you are using the online app), or until the Round ends (if you are on Prepd Offline).