To create a new group or edit the name of an existing group, click the (Create/Edit) link next to the Groups title in the sidebar on the left of the page.

This will take you to the "Edit Address Groups" screen. You can choose to provide a "Nick Name" and a "Display Name" for a group and then click on the "Add" button to create the group.

The "Display Name" is what appears in the sidebar on the left of the Address Book screen. The "Nick Name" is the name that you type in the To, Cc or Bcc line of the Compose screen to send mails to all members of that group. Both are required.

You can create multiple groups from the same screen. Once done, click on the "Save changes" button and on the "Address Book" link on the top to take you back to the Address Book screen.

Now in the left handside you can see the address groups that you have created with a "+" and "-" buttons besides each of them. The "+" button is to add to the group and the "-" button is to delete from the group.

To add contacts to or remove contacts from a group, click the checkbox next to the contacts you want to add/remove to select them, and then click the appropriate "+" or "-" button next to the group in the sidebar on the left you want to add the contacts to/remove the contacts from.

You can use the "Search contacts..." box to narrow down the displayed list of contacts if you want to find one quickly. You can also click a checkbox, then hold down shift and click another checkbox to select all contacts in that range, rather than having to click one at a time. You can also use the shortcut keys j and k to move the selection caret between contacts, and the x key to select/unselect a contact.

Lets say you created a group by specifying the "Nick Name" as "Friends". And you added a few addresses to this group as mentioned above.

You can then open a Compose screen and specify "Friends" in the To, Cc or Bcc field to have the mail send to the addresses in the "Friends" group.