--creat the login for the Active Directory User
CREATE LOGIN [mydomain\NewUse] FROM WINDOWS;

--switch to the right database: if more than one database, repeat for each one
USE SandBox;
GO
--Create the user to match the login
CREATE USER [mydomain\NewUser] FROM LOGIN [mydomain\NewUser]

--assign permissions
--put the user in the correct permissions role
exec sp_addrolemember 'RoleAlreadyCreated', 'mydomain\NewUser'

--an example in case you don't have the role with the right permissions yet:
CREATE ROLE [AlmostOwners] 
EXEC sp_addrolemember N'db_ddladmin',   N'AlmostOwners'
EXEC sp_addrolemember N'db_datareader', N'AlmostOwners'
EXEC sp_addrolemember N'db_datawriter', N'AlmostOwners'
--can the users EXECUTE procedures? comment out if false
GRANT EXECUTE TO [AlmostOwners]
exec sp_addrolemember 'AlmostOwners', ' mydomain\NewUser'