In order to access a Site via the Site drop down menu, a User must have a Site Role assigned to them at the Site level (either directly or via their Group association).
To see which Users/Groups have Site Roles assigned to them for a specific Site:
Navigate to Manage Site > Site Settings.
Click the Roles tab.
To assign a User/Group to a Site Role:
If the Site Role has already been added to the Site, click the Choose Users/Groups button to assign the User or Group to that Site Role.
If the Site Role has not been added to the Site yet, add it by clicking the Choose Roles button, then click the Choose Users/Groups button to assign the User or Group to that Site Role.
For more information on permissions in Cascade CMS, check out this article in our Knowledge Base.