Start the rice in the rice cooker. If you don't have a rice cooker, you can cook this on the stove. Combine 2 cups sushi rice with 3 cups water. Cook until tender.
Meanwhile, slice vegetables very thinly.
Mix together rice vinegar, sugar, and salt.
Scoop rice into a wooden bowl and with a wooden spoon mix in the vinegar, sugar, and salt combo. Fan the rice to cool off while stirring the rice. Bring the rice up the sides of the bowl to help cool faster.
When rice is cooled, lay out a seaweed sheet, shiny side down on top of the sushi rolling mat. You'll notice lines in the seaweed sheet, have them run vertically toward you. Spread a layer of rice on the sheet. Because rice is sticky, it helps to keep a small dish of water for dipping your fingers in.
Spreading the rice onto the seaweed sheet is best done with your fingers.
Place several thin pieces of your vegetables on top of the rice. Roll the sushi mat carefully while keeping it from rolling up in the seaweed sheets. You'll get the hang of this rather quickly. The goal is to keep the sushi roll firm and tight. When you get to the end of the sushi roll, wet your fingertips and run them along the edge of the seaweed sheet to help it stay closed.
With a sharp knife, cut along the lines in the seaweed or cut them as wide as you desire. Wipe the knife in between cuts as needed.