Questions related to field. Appropriately difficult relating to content knowledge. I'd recommend reviewing common questions for your specific field and pedagogical approaches to instructing in your specific content areas. I would not answer vaguely, but include specific examples from past teaching experiences.

The process was straightforward as I had previously been a Teaching Assistant and was a known quantity. They preferred to hire previous TAs over most other part-time applicants. I did have the implicit support of the Department Chair (who was ostensibly the manager for the position) and of the Calculus Coordinator, who developed, maintained, and guided the calculus curriculum and the teaching thereof for the department.