Bring water to a boil in a medium saucepan. Add rice, swirl to coat, then reduce heat to a low flame, and cover. Simmer until water's absorbed and rice is tender, about 18 -25 minutes. Drain off excess water.
While rice is boiling, mix vinegar, sugar, and salt in a medium saucepan and heat over medium heat. Stir occasionally to dissolve sugar and salt. Then transfer to a jar or dish and put it in the refrigerator to cool until the rice is ready.
When the rice is done, turn off heat and add the cooled vinegar mixture. Mix with a spatula or fork to avoid over-stirring. It'll dry as you mix and by the time you're done, it'll be dry and sticky.
Prep your veggies while you're waiting for the rice to finish cooking. Make sure they're finely sliced. If they're too bulky, they won’t work well in the sushi.
Now grab your sushi mat to start the rolling process. Top with a sheet of nori. Dip your fingers in water to keep them from sticking. Put a thin layer of water over the nori. If it’s too thick, it'll be too bulky for the sushi.
Arrange a generous serving of the veggies at the bottom ¾ of the sheet that's closest to you.
Roll nori and rice with your fingers. Once the veggies are covered, use the mat to compress the sushi. Continue until it’s all rolled up. Slice with a sharp serrated knife for best results. Repeat until all rice and fillings are used up. It'll probably yield 4 rolls.
Serve immediately with condiments of your choice. Although it's best served fresh, the sushi can hold up in the fridge for up to 2 days.