First, having the right amount of water will help greatly... I wouldn't start any turtle in anything less than 20 gallons, and general rule of thumb is 10 gallons of water per inch of carapace (top shell) length.
After correcting any issues with tank size, you will need to buy a filter... one that's rated for at least twice the water volume it will be filtering should do the trick. You will still need to clean the filter medium at least once a week, siphon out any solid waste that the filter misses, and do regular water changes.
(Other things you will need: Heat lamp, UVB lighting, Basking area that the turtle can get completely out of the water on, and perhaps even a water heater depending on how cool your house is kept... all in all, a proper setup for any aquatic turtle will run around $150 - $200... and you will eventually need a huge tank, or a little pond, as most sliders, at least the females, can reach about a foot long, and that 10 gallons per inch rule holds for their whole life.. which can be 25 - 30 years or more if you do it right.)
