Assigning database roles to user groups of the Windows Active Directory Domain is managed by means of SQL Server Management Studio functionality.

In order to assign a specific Role to selected User Group do the following: 

1) Go to MS SQL Server Management Studio. 
2) Connect to the SQL server instance, then go to Security -> Logins.
3) Find the User or User Group which you would like to add, right click and open the Properties window.
4) Go to the User Mapping tab.
5) In the upper list - select your database and set the flag in the corresponding check box. 
6) In the lower list - select the desired role. 
7) Press OK.