1. A sub-site can inherit permissions of a parent site. 2. If you want to set up a different permission set for the sub-site you need to "stop inheriting" the parent site permissions. Do that! 3. Create your groups and Add users to them. 4. Grant Permissions(levels) to your Group. 5. Use the Default permission levels (Full Control, Design, Read, Contribute, Limited Access) or Simply Create your own permission levels.