Choose your Project under a Domain -
Click on Project Users ----> click on Add ----> click on, Add From the User list ----> Select a User ----> Click on Arrow sign to assign User to a Project.
The only choices you have for setting a user's permissions on a specific project through Site Admin are to make them a Project Administrator or not. By default, when you add a user to a project through Site Admin they are granted only Viewer permissions. Through Site Admin to can also grant them the Project Admin permissions. If you want to do anything else with their permissions, like assign other roles to the user, you have to log into the project, go to Tools > Customize, select Project Users or Groups And Permissions, and make your modifications. You can also add users to a project through that UI.
This information is all available in the User Guide and Administrator Guide. You might want to review those.
(Opinions and information contained in this post are wholly my own and do not reflect the opinions of my employer.)