I was reached out by a professor to be their TA and it roughly took a week before I heard back from the college before I was give the offer for the position. Everything went decently smoothly.
Interviewed as a TA. It was a quick meeting with a professor. I had to demonstrate my skill related to the field and I had to demonstrate my teaching skill.
I applied through an employee referral. I interviewed at Arizona State University
Interview
Call from professor asking about my experience in the field and how confident I am to answer students questions and help them in labs. Not too hard, good course and good professor, and good university.
It is easier to get through if you make an acquaintance with the professor teaching a particular course of interest. The professor can recommend you to the hiring department and make the process much more simple. I did not have an HR interview as a result but just interaction with the professor