The quickest way to add users to a group is via the Manage groups area.
You must be logged in as an Administrator to manage groups!
Steps
Navigate to the Manage groups page from the navigation bar.
You will be presented with this page:
Find the group you wish to manage either by searching, or stepping through the paged response. The results come back in alphabetical order.
Click on the Name of the group.
Click the User access link at the top of the page.
Find the user you wish to add by either using the search (it will query both their name and email address).
Click the name of the user you wish to add.
You can scroll down the page to the user you have added and use the select dropdown to the right of the user to choose a permission level:
Once all the required changes have been made, click Save changes in the top right of the page.