Making sushi rice:
Start preparing the rice approximately 2 hours before you want to make the sushi rolls.
Wash rice, stirring with your hand, until water runs clear.
Place rice in a saucepan with water; soak 30 minutes.
Drain rice in colander and transfer to a heavy pot or rice cooker; add 4 cups water.
NOTE: To improve the texture of the rice, after rinsing, let the rice drain 30 minutes in the refrigerator before cooking.
If you don't have a rice cooker, place rice and water into a large heavy saucepan over medium-high heat; bring just to a boil, reduce heat to low and simmer, covered, for 15 minutes. Turn off heat and let rice rest, covered, for 15 additional minutes.
When rice is done cooking and resting, transfer to a large bowl; loosen rice grains gently with a rubber spatula or wooden spoon by cutting and folding (do not stir, as this will crush the rice). NOTE: Either use the rice soon after preparing it, or cover it with a damp cloth to keep it moist. Do not refrigerate the cooked rice.
Sprinkle the vinegar mixture over the rice, mixing together as you sprinkle (add enough dressing to coat the rice but not make it damp - you may not need to use all the vinegar dressing). Spread the hot rice on top of a large sheet of aluminum foil and let cool.
Preparing sushi ingredients:
Wash, peel, and seed cucumber. Slice in half lengthwise, then cut into long, slender strips.
Cut the avocados in half lengthwise, then remove the pit; cut each section in half again (lengthwise), and carefully remove the peel. Cut the section in long slender strips. Sprinkle the sliced avocado with lemon juice to keep from discoloring.
If you are using snow, crab, remove the crab meat from the thicker portion of the legs and cut in half lengthwise. If you are using imitation crab sticks, remove the plastic wrapping and cut each in half lengthwise.
Place the cucumber slices, avocado slice, and crab slices on a plate; cover with plastic wrap and refrigerate until you are ready to use.
Making the sushi:
Place the nori (dried seaweed) down first. Spread a thin layer, 3/4 to 1 cup, of rice over 3/4 of the nori leaving approximately one inch of uncovered nori at each end. Note: It helps to wet your fingers with cold water when you are patting the rice onto the nori.
Arrange strips of avocado and pickled cucumber along the center of the rice; top with battered/creamed crab meat.
Wrap the plastic wrap around the roll and set aside until ready to cut. Refrigerate or for longer storage. Repeat with remaining nori sheets to make additional rolls.