Hello,
Here is a link with all the necessary start up materials for a turtle.
http://www.redearslider.com/startup.html
It's important to have a water heater and proper basking lights, especially since your turtle is ill. All the other items are important as well, but heat is crucial for a sick turtle.
You are correct to assume that your turtle needs to see a vet. Make sure it's a herp vet and make an appointment ASAP. The sooner he gets in, the better his chances are.
Also, if the other turtle is not exhibiting signs of illness, you need to separate them. Most likely your one turtle has a respiratory infection, which is very contagious, so to prevent the other one from falling ill you'll need a second tank. A rubbermaid bin makes a great temporary home, and is cheaper than buying a second glass tank so look into that.