They are making this really easy for us nowadays. I remember how insanely hard this was back in the day.
Simply follow these steps from your Ubuntu machine and have your AD credentials ready. As long as your AD is working properly these are the steps you will need to take:
1. sudo apt-get update
2. sudo apt-get install likewise-open
3. sudo domainjoin-cli join fqdn.of.your.domain Administrator
4. sudo update-rc.d likewise-open defaults
5. sudo /etc/init.d/likewise-open start
After that is done, you can log out, then log back in with your domain\username account (You have to add the domain\ first).