In the 'Settings' tab on your management toolbar, click 'About this group'
On this page, there is a 'Logo or picture' section where you can choose an image to upload.
This image will appear in your group's sidebar and header, if you haven't uploaded a separate header or removed the sidebar in your 'Layout' page. It also shows up in group search listings next to the name and a brief description of your group.
Uploading a banner header
>>Upload a logo
Themes: Choosing the look and color of your group
Layout: Choosing content for your homepage
Customizing your group public profile
Customizing email templates