The staff member gave me yet another little piece of paper in return, and I was told that I could drive the car around into the testing lane.
Inside the building, I showed my driver's permit, car registration, and proof of car insurance, and my licensed driver showed their California license.
They do require your licensed driver to accompany you in line. I parked in one of the regular parking spots - not the ones reserved for those returning from a test - and went in the line for people with appointments. I drove to the DMV with my licensed driver and arrived 15 min before the test time (there's a sticker on my permit that says to do that). I thought I'd post a description of all the steps I went through for a behind-the-wheel-test at a California DMV recently (Santa Clara), for those who'd like to know exactly what to expect.