When downloading a team project, the user often needs to authenticate (at least with projects or part of projects hosted in private repositories), with a username and a password. If you are a team project administrator, you should provide the necessary instructions to your translators.
As of 2022: Since using 2-factor authentication at GitHub is not optional any more, you can't use your regular Github password to authenticate to Github repositories. For apps that don't request that next step in the auth process (sms code, confirmation on the phone or other device, code from the authenticator app etc.), services make it possible to generate a unique string that will act as your password. In Google, they call it application passwords, IIRC, GitHub calls it access token.
In a nutshell, your translator can use their Github password to log in to Github, but they need a personal access token to authenticate when pulling from and/or pushing to Github repositories as OmegaT does when they work on a team project (as well as for any other authenticated interactions outside of the web site). In other words, the personal access token associated with a github username is that user's password.
Here's how to obtain a personal access token (if you are a project admin, these are the instructions you should share with your team):
If you prefer, you can follow this video.