When a new user is created or added to a new project, they are granted certain default permissions. These permissions will be the same whether you are an existing user added to a project, or a new user that has been created by an existing user.
The default permissions for every user in a given project are 'View labels' and 'View sources'.
These essentially grant you the ability to access (non-sensitive) datasets within that project and see the verbatims (which belong to sources) as well as the labels associated with those verbatims.
These permissions will not grant you the ability to apply or remove labels within a dataset. To be able to do this, among many other things, you will need to be granted additional permissions by another user within the project that has the 'Modify users' permission.
If you are accessing Communications Mining via Automation Cloud, then admins on your cloud tenant will automatically have Admin access on Communications Mining. This will grant them admin privileges on 'Sources permissions', 'Datasets permissions', 'Streams permissions', 'Users permissions', 'Buckets permissions', 'Integrations permissions', and 'Utility permissions'.
For a more detailed explanation of the different user permissions, see here.
To understand more about how to update a user's permissions, see here.