As it turns out, this is more simple than you would usually figure. All you do is the following:

• Go to Site Actions/Site Permissions.
• Then, check the box which is to the left of the group you need to edit.
• In the Ribbon, click the ‘Edit User Permissions’ button (also works for individual users).
• Adjust the permissions as needed and click the OK button.

Voila! You’re done.