For the Rice: Wash rice in cool water until water runs clear. Drain excess water. Place rinsed rice and 1 ½ cups water in a pot. Bring to a boil. Cover and reduce heat to low. Simmer 15 minutes, or until all water is absorbed. Remove from heat and let stand, covered 5 minutes.
Rinse the rice in cold water while stirring briskly. Drain the rice completely.
In a medium saucepan, bring the water to a boil. Add rice and cover with a tight fitting lid. Reduce heat to low and simmer 20 minutes, or until all liquid is absorbed. Meanwhile, in a small bowl combine vinegar, sugar and salt. Stir until completely dissolved.
When rice is done, spread evenly on a well-greased cookie sheet using a spatula or rice paddle. Sprinkle the rice with prepared dressing while mixing with spatula or rice paddle. Keep the rice covered with damp paper towels or napkin until the rice is ready to use.
Slice tuna into thin pieces or small cubes.
Slice avocado into thin slices.
Pass nori sheets over an open flame briefly to lightly toast, if desired.
Place the seaweed on a bamboo mat, then cover the sheet of seaweed with a thin even layer of prepared sushi rice. Smooth gently with the rice paddle.
Layer tuna and avocado on the rice, and roll it up tightly. Slice with a sharp knife.
Serve with soy sauce, wasabi and ginger.