First you need to figure out what functionality you want to cover by your permission system, and in what detail:
Access to tables (List, CRUD)
Functions/Modules
Access on record level (=ACL)
Positive (grant) or Negative (revoke) semantics
What is the "admin" role allowed to do
If you want to restrict access to tables, you can easily set up an additional table containing all the table names, and grant select-list/select-record/insert/update/delete access to the roles/groups, as sketched by JV.
If you want to grant access to functions or modules, have a table of modules and grant execute to roles/groups.
Both functionality is equivalent to grants in SQL.
Access restriction on record level is much more complicated, as you need to model access rights on the status of a record (e.g. "public", "private", "released" in CMS apps), or have explicit permissions on each record.
If you want to implement a permission scheme equivalent to NTFS, you calculate the permission per record based on the group the user is assigned to, and have user-specific permissions that may override the group permissions, and revokes overriding grants.
My applications typically work on table+function / group level, which may be good enough, depending on your requirements.