I love making sushi - only learnt how to make it a few weeks ago. Firstly you need the right sort of rice. When I haven't been able to get sushi rice I've been okay with a thai short grain rice. I put it in a pan with 2 cups of water to each cup of rice and let it soak for about 30min or so. Then cook it with the lid on until it has absorbed all the water. Then stir in some sushi vinegar and let it cool. Then I take a sheet of pretoasted nori and spread the rice out on it, keeping it about an inch away from both short sides to give it space to roll. Then I put strips of cooked carrot or whatever I fancy in the middle. Roll it up and dampen the edge of the seaweed to make it stick together. And then slice it, and serve with pickled ginger or wasabi (japanese horseradish).
Some of the ingredients can be hard to find - I know where to get them in the UK, but I can't help with elsewhere. And before I bought a bamboo rolling mat I did okay with a clean teatowel.