When I was younger, eating at an authentic sushi restaurant was intimidating. Unless I was with the "adults" who knew how to behave, I had no nerve to sit at the counter.
"Real" sushi restaurants are the places for adults. I realized that I became "old" when I found myself relaxed during a dinner at a sushi counter. Well, it is a good thing. Young people who lack experience naturally feel uneasy there.
If you are with little children who may scream around during the meal, it would be safer to take them to kaiten-zushi, or sushi restaurants with a rotating sushi counter. Don't worry, many kaiten-zushi today are family-oriented and more reasonable, yet the quality is not bad at all.
At many sushi restaurants, there are tables as well. If you don't know much about sushi, you might feel more comfortable at the table, but I strongly recommend you to sit at the counter, where you can see the art of sushi making. You can decide what to eat by observing the "catch of the day" in the glass showcase or through the conversation with the chef.
There are no rules about ordering sushi, but for dinner we often start with sashimi (thin-sliced raw fish) or other small dishes, and because sushi rice makes you full fast. Of course we can eat sushi only, but it is not a very cool behavior.
When you sit at a counter, order something to drink first. Beer, dry white wine and sake go very well with seafood. If you don't like alcoholic beverages, you can ask for free hot green tea.
At the counter, it is normal to order sushi to the chefs behind the counter directly, although you can ask for other things such as drinks to a waiter/waitress as well. When the chefs are talking to other clients, you should not interrupt their conversation, but don't hesitate to make your order when they are working on something. You can simply say, "Maguro onegaishimasu (Tuna please), " for example.
I'll explain more about fish in the next post.