I basically do three things when interviewing...
(1.) Ask them the, "Tell me about yourself/walk me through your CV" question. Mostly let them narrate to see if they have prepared their talking points for this or not... if they have, great, if they have not, that is not the best of sign to start things off.
THEN
Intentionally interrupt them to screw them up. See if they can think on their feet. Do not entirely let them narrate what amounts to a planned, practiced speech.
This really murders some people coming out of business school, where preparing that canned speech is a thing. I want to make sure they did it but, once it is done, or at least clear they did it and did it well, I want to see how they take a rogue wave.
(2.) After that, I am usually done asking about work stuff. Just try to get to know the personality, the likes and dislikes, and see if they would fit in with people.
This oftentimes comes down to college sports.
(3.) If they promise particularly quantitative skills, then I'll stick them in front of a computer and make them demonstrate it for me. Write me the particularly Excel formula, the particular macro, or the particular R script that I want. Prove it or do not.
...then we are done.
