There are two ways to do this: by going through a Judge Profile, or by going through a Competitor Profile. 

First Way: Modify Judge Profile
Navigate to the Judges tab. Find the Judge in the list and click on their name. In the popup, click "Assigned Competitors" (a black box). Click "Assign" next to any Competitors you'd like to add.

Second Way: Modify Competitor Profile
Navigate to the Competitors tab. Find the Competitor in the list and click on their name. In the popup, click "Assigned Judges" (a black box). Click "Assign" next to any

Judges you'd like to add.

You can make changes before, during, and after a competition, as well as before or after the RocketJudge auto-assignments are made (learn more about that here).