At a sushi counter the chef shapes each piece for the moment it reaches you. The rice is warm, the fish is at its best temperature, and the seasoning is already balanced. The simplest manner is to eat each piece soon after it is placed in front of you.
Hands or chopsticks are both fine for nigiri. If you use soy sauce, touch the fish side, not the rice, so the rice does not fall apart. Many chefs already brush on sauce, so taste first. Do not dissolve wasabi in the soy sauce. Ginger is a palate cleanser between pieces, not a topping.
Be considerate of the small space. Arrive on time, cancel early if plans change because many counters have few seats, and mention allergies when booking. Avoid strong perfume, which interferes with the aroma of the fish, and ask before taking photos.
Tipping is not expected. At an omakase counter, trust the chef and avoid asking for changes to the order. If something is not to your taste, say so politely when you book. A simple thank-you to the chef is always appreciated.