Rinse the sushi rice under cold water until the water runs clear.
In a rice cooker or saucepan, combine the rice and water. Cook according to the rice cooker's instructions or bring to a boil, then reduce heat to low, cover, and simmer for about 18-20 minutes until the rice is cooked and the water is absorbed.
In a small bowl, mix the rice vinegar, sugar, and salt until dissolved. Gently fold this mixture into the cooked rice, then let the rice cool to room temperature.
Place a bamboo sushi mat on a clean surface and cover it with plastic wrap.
Lay a sheet of nori, shiny side down, on the bamboo mat.
Wet your fingers with water to prevent sticking, then spread a thin, even layer of sushi rice over the nori, leaving a 1-inch border at the top edge.
Arrange the cucumber, avocado, sashimi-grade fish, and any other desired fillings in a line across the middle of the rice.
Using the bamboo mat, carefully roll the sushi away from you, pressing firmly to create a tight roll. Moisten the top edge of the nori with a little water to seal the roll.
Using a sharp knife, slice the roll into bite-sized pieces. Wipe the knife with a damp cloth between cuts to ensure clean slices.
Arrange the sushi pieces on a plate and serve with soy sauce, wasabi, and pickled ginger on the side.
Enjoy your meal!