I don't want to step on any feet here, but turtles are what I do so I thought I would share my knowledge.
Here is a list of some of the basic things you will need for your turtle.
The Must haves
A tank. This should be as big of one as you can afford. It can be either a glass aquarium or a Rubbermaid container. You should have 10 gallons of water for every one inch of shell. For example a 10 inch female RES would need a 100 gallon tank. This goes for all of the turtles in your tank. If you have two 4" RES you would need a 80 gallon tank to make them happy. That would give them room for their own territories. Do research on the turtle you are getting to see how big they are going to get so you can determine how big of tank you will need. Some good starter tanks are the 20 gallon ones sold right here at turtlesale.com.
Lighting. You will need a good UVA/UVB bulb, most are Fluorescent. Repti Sun by Zoo Med is a good bulb for this. You will also need a bulb for a basking spot. This can be a regular bulb or a flood light bulb depending on your tank size. The basking spot temp should be around 90 degs. There are some bulbs on the market called Mercury Vapor Bulbs that give off heat and UVA/UVB, they run around $30 but many people swear by them.
A basking spot. This can be as easy as a rock or some people make enclosed platforms on the top of their tanks. There are turtle docks on the market too, but most turtles will out grow these within a couple of years. The most important thing is to be sure that it is dry and easy for them to get up onto.
A Good Filter. Turtles are messy animals and need a strong filter. Most people get the canister filters like the Magnum 350. The bigger you can get the better.
A Water Heater Depending on where you live it is a good idea to have a water heater in the winter months. Most turtles like temps around 78 degs. Do research to see what water temps your turtle requires. There are many heaters on the market that work well for turtles. Submersible, strong ones are best or you can use an under tank heater which is what I use.
NO Gravel Although gravel looks nice you shouldn't use it in your turtle tank. They can ingest it and become impacted. Also it helps hold waste in the tank making it harder to keep clean. If you really want gravel use some that is larger then their head so they can't eat it.
Extras
Plants These aren't a major need, but a good idea especially for hatchlings which like hiding places. You can use either real ones (found at most fish stores) or you can use plastic or silk. Just be sure the plastic ones are strong so they can't rip peaces off and ingest them.
Large Rocks or Slate This helps break up the bare bottom look and also gives the turtle some traction under his feet.
For feeding a good pellet food like Reptomin should be the staple of their diet. Also offer some greens like Romaine lettuce, collard greens and duckweed. You can also offer live foods like snails, feeder guppies or rosy reds (not goldfish they are to fatty and often medicated) and earthworms. I would advise against feeding them dog food. The red dye in dog food has been found to make reptiles sick and even cause death.
I'm just a turtle basking in the sun.