From your game schedule and the "Officials and Workers" tab, you can publish a single event at a time by click the blue 'actions' button (three dots), and then click to "Publish Assignments".

If you'd rather publish multiple events at the same time, you can do so by clicking the checkbox next to each event (or multi-selecting all events on the screen with the single checkbox at the top left of the schedule). Once you've selected all events that you'd like to publish, you can then publish the assignments on those events by clicking the "Actions" button at the top of the screen and selecting "Publish Pending Assignments".