There is a free package available that makes connecting a Linux client to a Windows Domain for authentication really simple - it's called Centrify. It takes about 2 mins to set up and (for me anyway) 'just works'.
Good have a look:
Centrify Express is a comprehensive suite of free Active Directory-based integration solutions for authentication, single sign-on, remote access, file-sharing, monitoring The #1 Choice for Active Directory Integration and cloud security for cross-platform systems. It is the quickest and most proven solution for integrating UNIX, Linux and Mac systems with Windows, and delivers more functionality and more to upgrade to when compared to other free offerings.
Setup info here (for Ubuntu):