I did this about a year ago, with DD who was 7 at the time. DD LOVED THIS!
We started off with talking, and a little education in the Penguin exhibit, as well as the Puffins. We had a group of maybe 12 people, including our family of 3. Backstage we were divided into 2 groups - our group got to visit with a pair of Puffins first, in an office/work room area. We were not allowed to touch the puffins but they were hilarious. If you have a choice, offer to see the Puffins first. I can't remember how long we got, in each, but it seemed fair.
Once the groups switched places, we were escorted into the backstage area of the Penguin display. For our group there was a smaller penguin out - I forget what kind he was, (rockhopper maybe) but his name was Freckles. DD had a ball! At one point, she was petting Freckles, and he started nibbling on her hair. We made sure the trainer knew about it, but he didn't put a stop to it. She was thrilled and still talks about Freckles. One of the larger emporer penguins was at the gate hamming it up for us too.
During the penguin backstage portion, I found the trainer realized that this was "the big ticket" for the group and while he was informative, he also stood back and just let everyone pet the penguin and get their photos.
I have seen other's photos where they had a bench and the trainer had the penguin up with them. For us, we had to grab the photos as we could. At one point, I almost wound up sitting in a bucket of fish for the sake of a good picture.
Just remember that it will be COLD in the penguin encounter area. I tend to carry a light sweater with me for Air Conditioning and DD had it on the whole time. By the time our time was up, we were cold enough that we were ready to go warm up.