I can only describe how it worked at stixrud.
On the first day, it was just DH and me meeting with the psychologist. He already knew, generally, what our concerns were, so he asked focused questions to get the information he needed. This meeting lasted about 90 minutes.
On days 2 and 3, my child went back with him and I stayed in the waiting room. DC didn't tell me much about the testing, but it was IQ-type testing -- puzzles and describing pictures, etc. Based on DC's attitude at the end of breaks, it wasn't anything she minded doing.
A week after the testing was done, DH and I went back (without DC) to get the results verbally and ask questions. We met with the psychologist for about 2 hours. We got an explanation of how she did on the various tests and what diagnoses that meant.
4-6 weeks later, we'll get the written report.