GRANT syntax for domain\user

Assuming you have created a user in this database associated with the AD login, e.g.

CREATE LOGIN [domain\user] FROM WINDOWS;
GO
USE your_database;
GO
CREATE USER [domain\user] FROM LOGIN [domain\user];
GO

Then you merely have to follow the same syntax. Because \ is not a standard character for an identifier, you need to escape the name with [square brackets]:

GRANT SELECT, INSERT, UPDATE, DELETE ON dbo.Tablename TO [domain\user];