I am using groups on my site to control access to areas and forums and the like. Nothing new or exciting there. I am using the groups more like attributes for users.
For example:
A person can belong to
"Registered Users"
"Parents" <<< This is the 'base' class
"Board"
"Executive Board"
"Truck Crew"

I am however having problems understanding just how this ultimately works out for specific module permissions. Assuming that I specify the permissions for the 'base' group, do I need to replicate those to the other groups and then add/delete specific permissions? In this example, being a "Board" member allows access to specific private forums.

Assuming that the permission sets were different, in this case, which permission set would be used?

when you are in the group configuration area in the admin panel, you will see checkboxes for all of the installed module. ideally you want to have your entire site setup and configured how you want it to be for public use and have all the module you decide to use installed. from there, you need to determine what you want each group to have access to (write it out is easy). In the properties for each group, check the boxes that correspond to the blocks you want group to have access to, and the module you want them to access. Forget about how the groups relate to one another, because they don't. For example (i will use my site as a relational factor):

Registered users only have access to very basic things like faq, partners, news, forum, and links, and no special blocks.
Basic members have access to all that plus the gallery, sections, and freecontent module, and can see 'top' blocks.
premeire members have access to all of the above plus downloads, module A and module B and all blocks other than those reserve for admins such as waiting content etc.

In addition to that, some modules allow you to control rights to subsections within them, such as Xgallery, wsproject, and so on, so you would set access control separately there if needed.

I hope this make sense to you. My english is not #1 so I have articulated to the peak of my ability.

Thanks for the explanation. If I may continue your thread using your site example, let me try to use set notation and see if I got this straight

Premiere Member is a subset of Basic Member
Basic Member is subset of Registered User

Therefore every premiere memeber is also a registered user.

Now, when you set up the group permissions, did you copy all Registered User permissions to Basic User and then add the additional permissions? Or did you just define the additional permissions?

I ask because it seems the second way works on my site. This leads to the question of just how permissions are applied. It appears that the results from the query are 'ORed' together to create a composite permission set.