The hiring and interview process was extremely simple. My professor suggested that I become a TA at the end of the semester and gave me a recommendation. It's been a few years, so I can't remember the specifics. I think I just filled out a really simple application and was basically guaranteed the position. I think they also did a background check. I then had to fill out some paperwork for payroll and was set. You have to "re-apply" each semester (you really just let them know you're coming back so they know whether or not to keep you in the system).
After being a TA for 1.5 years, I was recommended for the teaching intern (TI) program. This program is fantastic. If you and the professor get everything figured out right, you can get a great experience and feel for what it is actually like to be a professor. You have a lot more responsibility and do a lot more work, but it is worth it.