First you need to create a login to the SQL Server for that domain group. In Management Studio connect to the SQL Server in the object explorer. Navigate to the ServerName > Security > Logins. Right click on Logins and select New Login. Select the Windows authentication radio button and click the search button. Type in the name of your domain group and click Check Names. It should find it, then click OK (you may need to click advanced to get it to search easier. After you are back on the New Login screen select the User Mapping page on the upper left.
Put a check mark next to the database you want to give them access to, and in the box below select the role or roles you wish to give the users access to.