How do I create new permission groups in SharePoint?
Click on the Cog symbol and choose Site Settings
Click on Site Permissions
Click on Create Group in the menu across the top
The Create Group screen will appear:
Give the group a name (e.g. My Site Members)
Ideally set the Group Owner to be your owners group – i.e. My Site Owners (this avoids problems in future where the owner of a group has left, etc)
Scroll down to the bottom and tick the appropriate box for the permission this group has to your site e.g. Contribute. (You can create a group here that doesn't actually have any site permissions by leaving all the boxes unticked. This is useful if you want to give a group permissions on a document library or something else – you have to create the group at the top level, but then you could give that group permission on a document library later)