First, cook the sushi rice as directed, and add a dash of rice vinegar if desired. I prefer mine without. While it's cooking, prepare what you're going to use for fillings (for example: sliced avocado, baked sweet potatoes/yams, fried tofu, sliced cucumber, julienned carrots, green beans)
Once the rice is cooked, let it cool for a few minutes. I find it easier to work with when it's warm but not too hot. It's pretty much impossible with cold rice. Lay out a sheet of roasted nori on a bamboo mat.
Scoop a spoonful of rice onto the nori and spread it out, flattening it as you go. You could use your hands here but the rice is really sticky!
Leave the very top edge bare as you'll need it to hold the roll together. Moisten the top edge with a bit of water. More rice = a thicker roll, less rice = a thinner roll. Make sure you go all the way to the sides or you'll end up with the slices on the ends being hollow and not pretty.
Put your veggies or whatever your're filling it with on top of the rice in a horizontal line. You can put them in the middle or at the very bottom edge. It's going to get rolled up so it doesn't really matter, as long as it's not at the very top.
Roll up the nori using the bamboo mat and add a bit of pressure - you want the roll to be tight, but you don't want to squeeze it so hard that the veggies are forced out of the edges. Don't get carried away and roll up the mat into the roll. When I was living in the Dominican Republic I couldn't find bamboo mats and I made the rolls just fine without it. You're pretty much guaranteed to find them at any asian market.
Alternatively, you can make rolls with the rice on the outside. This is a bit more tricky, but with the help of some plastic wrap it isn't too hard. You don't have to use plastic wrap but the rice is really sticky and for me it always gets stuck to the bamboo mat and all over my fingers.
And finally, you're ready to dip it in some soy sauce or Braggs or whatever you like, and enjoy :)