To assign Roles and Rights to a User go to his profile and click on "Administrate Rights..." (see screenshot below).
System´s roles are defined in the panel 'Roles'. Check those you want to assign to the selected user. After saving all appropriate permissions are active for this user.
Rights always are applied to a particular object. Theoretically, you should first select an object, and then the rights you want to assign to the selected user for the selected object.
But because of the large number of objects AxCMS.net maintain (40.000 pages/documents in one system is a usual use-case), assigning rights occurs via Categories. I.e. you create categories, assign your objects to categories and give the users rights for categories. Users get the rights for all objects in the selected category and below.