we had a clinical psychologist (phd) evaluate our children for social issues/aspergers and adhd. The evaluations included some intelligence testing since that makes up a major part of one's psyche, I suppose.

what occurred:
there was a patient intake session, where we parents discussed our child, strengths, weaknesses as we saw them, and any issues with the dr.
there was a session where the dr interviewed each child. there were many forms for us to fill out for personality, mood and behavior ratings. we also had forms to give to teachers for the dr. to understand the behavior from that perspective.
there were forms for the kids to fill out -their own mood and personality rating forms - this may occur more when a child is older than when they are quite young. My daughter was asked to make some drawings. My son was not asked this, I suppose because he is older.

There was intelligence testing, and some other testing done, including a very boring computer test (to test for inhibition and attention).
all this was scored, reviewed and evaluated. in the case of the kids' doctor we received very lengthy report about what all of it meant.
The insurance did pay for a large part of it, as there was in both cases a diagnosis, even though the dr. was out of network.

My husband also had this done recently for himself, with an in-network doctor; the process was pretty similar, but with a somewhat less in depth final report. the insurance paid for all of it with the exception of a couple of small copays.