Supporters is not Groups based and does not interact with Groups, though you could restrict viewing to a group you generate separately for Supporters.
Supporters is an admin tool to manage your Ranks so that they reflect donations from your Supporters.
Supporters is not a standalone module - it is a companion to Treasury.
Its main purpose is to highlight disparities between your proposed ranks (based on minimum donation levels) and the actual ranks you define through the DragonflyCMS ranks system.
It can also be used to display your Supporters list to members, depending on the viewing permission you give the module. Admin columns are hidden from non-admin view, although individual Supporters will see their own information.
The rank_value field has been added to your Core bbranks table and is used to determine if your users have been assigned an accurate rank according to their level of donations.
Your first step is to edit the special ranks that relate to your donations and assign a minimum value for each of those supporter ranks. (you can also add special ranks in this area - deletion is deliberately omitted)
Your second step is to open the Supporters module - clicking on the red change button will automatically change that user's rank and will immediately return you to the Supporters list where the Current Rank will display the green button.
The current pagination default is 15 supporters per page - to change this, modify the variable $supporters_per_page on line 11 of modules/Supporters/index.php.