What you will need to make sushi at home:
a tub or large dish to cool rice
a spatula to turn and spread rice while cooling
bowls for ingredients
cutting board
sushi rolling mat
knives
Depending on how Oriental you want to make your sushi dinner, you may also want to add some of these things to your sushi experience:
geta (wooden sushi trays)
sushi serving dishes
condiment dishes
japanese omelet pan or square cast iron skillet
Sushi ingredients are so varied that it would be nearly impossible to catalog all of them in one place. For simplicity's sake I'm only going to list the ingredients normally used to make sushi in your own kitchen.
Sushi rice Rice for sushi has to be glutinous (sticky) and should be short or medium grain. Most Japanese style rice available at grocery stores will suffice. I've been using Nishiki lately and I like it quite a bit. You can use brown rice, but it takes a bit of practice because it's not nearly as sticky as white rice.
VinegarUse a rice vinegar. If you must, you can substitute white vinegar for rice vinegar.
Soy sauce WasabiLook for real wasabi in better asian food stores and online rather than the cheap imitation.
GariPickled ginger, it's used to clean the pallet between bites of sushi. Can be found in most asian markets and many grocery stores.
NoriSeaweed is used extensively in Japanese cooking and is used in most types of sushi. Make sure you buy enough of it, in case you make mistakes at first.
Fish Fish is the main showcase ingredient in most sushi. Make sure if you're using raw fish that you select a good grade of fish. Ask the person at the counter where you buy your fish if he has any sushi or sashimi grade fish. Small pieces of shrimp or crab work well for this, too.
Fruits and Vegetables Most any sort of vegetables you want are acceptable in sushi -- avocado, baby daikon sprouts, cucumbers. Leaf lettuce in a roll gives a nice ruffled appearance as it peeks out of the end pieces. For vegetarian nigri, you can use steamed asparagus or other stalky vegetables.
Fruits can also be used in sushi. For a slightly sweet dessert, try making apple or kiwi sushi.
You may also want to have a few sesame seeds on hand for the outsides of the rolls or to add crunch to the inside of a roll. Just about anything you can fit inside a roll will work so once y ou become accustomed to the process, you can really begin to experiment depending on your own tastes.
What to do:
Cook your rice first, use a good sticky sushi rice. Let your rice cool and then you are ready to begin.
Choose your fish or mix your filling. If using a pice of fish, such as shrimp, tuna or crab, you do not need to mix a filling.
An easy fillingOne can of tuna fish
One tablespoon of mayonnaise
One teaspoon of chili sauce
Start by cutting a sheet of nori in half.
Place your half sheet of nori on the rolling mat.
Moisten your hands and spread rice onto the nori using your hands. Leave about 1/2 an inch of the nori bare. Beginners may find it's easier to leave a bit more than that. Spread some wasabi along your rice.
Add your ingredient-- either fish or the mixture.
Holding the mat with both hands, carefully roll the bottom end over the filling, taking care to squeeze and compress evenly across the entire roll.
Continue rolling the nori around the rice and ingredients until the bare nori seals itself. If it doesn't seal on its own, use a slight bit of water or vinegar to seal the edge off.
If your knife is sharp enough, cut the roll in half now. If your knife isn't the greatest, put the roll in the refrigerator for a few minutes. This allows the roll to harden slightly to make it easier to cut.
Once cut in half, place the two pieces on top of each other.
Continue to cut the roll into six pieces by cutting through both halves at once.
It's bad luck to cut a roll into four pieces, and six is the standard amount 
