My personal experience is that you aren’t going to save much doing it at home. It requires going out and buying a lot of very specialized ingredients, as well as extremely fresh fish. Not to say you shouldn’t do it, but it’s unlikely you’ll see a big cost savings when you could just spend $6 per roll.
Buy good ingredients from a good Asian store. A lot of big chain stores sell the stuff as well but it’s unlikely they have enough turn over, so the ingredients will likely be old and a bit stale. Like I said, this isn’t something you want to try and skimp on. If you buy a bunch of no-name-brand ingredients your sushi will taste like crap.
Buy the sushi grade rice then follow the instructions on the bag (some people add stuff when the rice is cooking, I’ll add a touch of vinegar and a bit of salt). As mentioned above it needs to cool some what slowly while being stirred with a paddle. Mix equal parts* rice vinegar and sugar with a heavy pinch of salt then bring to a boil. When the rice is done put it in a large bowl, drizzle the vinegar over it, then gently fold to combine. You need to do it gently so you don’t squash the rice.
*typically it’s about 1/4 cup vinegar, 1/4 sugar, then anywhere from 1 tsp to 1 tbls salt for two cups of rice. Try this to see if you like it, then you can adjust it for the next time you make it. Each person has their own preference for sweet, sour, or salty.
Once the rice is cool keep it covered with a damp cloth. And don’t try to store this for a couple of days, it gets worse with time.
When it comes time to work with the rice, put a large bowl of water with some vinegar in it. Then keep dipping your hands and tools into the water. The rice is going to be VERY sticky, so you’ll need the right amount of water to keep it from bonding instantly to your hands and knives.
A paddle for folding the rice. A nice long sharp knife. Two cutting boards, one for raw fish the other for everything else.
You’ll need surprisingly little fish. Then grab what ever extras you like: fake crab, those long mushroom things, cucumber, avocado, spicy mayo.
That’s about it. Not really that much to it. Put your nori on the mat. When your hands a bit then grab a ball of rice. Flake it over the nori leaving about an inch strip at one end without any rice on it. Lay your fish and ingredients in a line on the other end, then roll. When the bare strip of nori to make it stick. After it’s rolled use the mat to press the roll into your favourite shape, I like triangles. Cut and serve.