Rinse the sushi rice in cold water until the water runs clear. Then, add the rice and 1 1/4 cups of water to a pot and bring to a boil.
Once the water is boiling, reduce the heat to low, cover the pot, and simmer for 15-20 minutes or until all of the water is absorbed.
While the rice is cooking, mix together the rice vinegar, sugar, and salt in a small bowl.
When the rice is done cooking, transfer it to a large bowl and add the vinegar mixture. Stir gently to combine.
Lay a sheet of nori seaweed on a sushi mat with the shiny side facing down.
Spread a layer of sushi rice over the nori seaweed, leaving a 1-inch border at the top.
Arrange the salmon, avocado, and cucumber strips in a line across the middle of the rice.
Use the sushi mat to roll the sushi into a tight cylinder, using the border of rice at the top to seal the roll.
Repeat the process with the remaining nori, rice, and fillings.
Once you've rolled all of your sushi, use a sharp knife to slice each roll into 6-8 pieces.
Serve the sushi with soy sauce, wasabi, and pickled ginger on the side.