I know a little bit about turtles from a past job. I can list a few things that will get you started in setting up the environment. All this I'm about to type I know from experience and what I learned from working in an aquatics store. Some may do things differently. But here are the essentials.
1) A glass aquarium 40-50 gallon would be best. -- Sliders can grow be to 10"+ in diameter if my memory serves me right, so the more room the better to have a healthy turtle.
2) A water pump; undergravel filter and a submerssible filter. -- Since sliders are both aquatic and terrestial they need half of the tank to be aquatic (full of water). A lot of people don't realize how dirty turtles are. They are very very dirty. They produce a lot of waste. So having a very good filtration system for the water is crucial. If it is not properly filtered bacteria can fester and ammonia levels can rise causing health problems and an unhealthy turtle.
3) Aquarium gravel & "basking ornaments".-- You need aquarium gravel to build a gradual incline for the turtle to get out of the water as it pleases. If you do this properly you won't need very many basking ornaments since it will have easy access to get out of the water completetly. If for some reason you can't accomplish this the way you would hope you can get things such as soft rocks or smooth logs for it to climb up on. You must have a option for him/her to know be fully submerged at all times though. **A good rule of thumb is it's a pound of gravel per gallon.** Since you are getting it as a baby be very careful to think of what the little one can and can't climb on. At this stage the best things are from nature itself, to save $! Plants also help turtles I would do fake ones at this point since your new to the turtle game.
4) A basking lamp/light -- Turtles are cold blooded therefore they need some form of uv/uva light to stay healthy and keep a hard shell. Depending on the size of aquarium you buy all depends on the wattage of light you buy. I can't remembe what wattage would be proper though. I THINK a 75w will be fine. Some will recommend a heating lamp as opposed to a basking lamp. I don't really see the benefit in that since a heating lamp will only provide warmth as opposed to a basking light which will provide uv/uva light that turtles need to survive. Turtles bask during the day and lay kind of "dormant" at night, there are light bulbs specifically for "night basking" also. That is a sigh of relief to some people seeing as how they don't have to have a bright light on in their house 24/7.
5) Water thermometer & terraruim thermometer -- I would recommend getting a thermometer first and monitoring the temperature of the water. The temperature of the water should be between 70-80 degrees I believe. Since you will have a heating lamp the temperature in the tank will rise therefore raising the temperature of the water so sometimes a water heater isn't necessary if you can keep the temperature stable. A terrarium thermometer measures the actual basking temperature of the tank this temp. Should be 80-90 degrees but don't quote me on that, it's been a while for exact numbers and I would look that up. The humidity of the tank should be nearly 100% though. A bottle to mist the tank occasionally will help w/ that.
6) Food (of course!). Sliders are omnivores. Buying meal worms, crickets, vegetables, fruits are all things a slider will pick at. Just try different things even food specifically for sliders and see what it likes best but always give him an option. When it is about 6" you can offer feeder goldfish.
7) Water conditioners and water test kits -- The conditioner is just take the chlorine out of the water so it is safe to swim in and conditions the water. The water test kits will test for nitrate, nitrite, ammonia, ph, alkalinity, and......er I can't think of the others, oh, hardness. Ammonia is the major one you have to worry about since I mentioned above they produce a lot of waste.
I know once I go to bed and wake up tomorrow I will remember something else. That's all I can think of right now. I will say having and PROPERLY caring for a turtle is a hard task, most people don't realize that. The initial set up of a proper environment can get expensive also, but after everything is peachy all you have to spend is on food. Remember to be very very careful if your buying a very young turtle since their shell has not completely hardened and any slight trauma to it can be fatal. They do squirm around in a palm of a hand so make sure you have a cushion should a fall occur. Make sure to wash your hands BEFORE AND AFTER handling your turtle. Bacteria on your hands can be harmful to a turtle. Also, turtles are/can be carriers of salmonnella (sp?). Like I said everything I just listed is from what I have learned. Hopefully this helped you out a little. And if you do it right and do as much research on it as you can your turtle can live for 10+ years! Good luck with everything and if you have any more questions feel free to ask!
(P.S- Wow! I really can't believe I typed all of that, it took me a while so I really hope it helps!)