Hi Mike,
Counselors vary in their techniques, so there's really not a 'normal' or 'typical'. I saw a psychologist who specializes in addiction/alcoholism. The first appt was more of a "why are you here? What do you hope to accomplish" type meeting, the next couple were examining my past from childhood on up to try to uncover anything to address there. He recommended a few books, and read them as I did and we discussed chapters in them. We talked very little about my drinking other than at the start of each appt a check in to be sure I hadn't since our last meeting. He taught me how to deal with anxiety and fear, sadness and celebration..sober. We did some guided relaxation exercises, meditation, and talked about how I would handle events in my life that would inevitably 'bring you to your knees'. I saw him for a little over 6 months.
It was really scary saying out loud why I was there, the extent of my drinking.. but he had heard it, and he was compassionate and understanding, never ever judged me.