Red Eared Sliders

The Tank
Red eared slider turtles are semi-aquatic and spend a significant amount of time basking, so need a tank that provides both water for swimming and an area where they can get out of the water for basking. A 20 gallon tank is considered a minimum, though larger turtles will need a larger tank to provide ample swimming room (see below) so even if you have a smaller turtle you might want to invest in a larger tank to allow room to grow. You do not need to use an aquarium though - large plastic containers or storage tubs are fine as long as you don't mind not being able to view the turtles from the side. As long as the tank is tall enough and the basking area is positioned so that the turtles can't climb out you won't need a lid.

The basking area can be provided by stacking smooth rocks, sloping smooth large gravel to one side to make a land area, or using wood (fixed or floating). However you design the tank though, keep in mind that turtles are messy and you will need to clean the tank frequently. No gravel is required in the tank but if you choose to use it make sure it is large enough that it won't be accidentally eaten.

Water and Filters
Red eared sliders need an adequate amount of water to move about and swim a bit. You can judge if there is enough water by looking at the length of your turtle. The water should be at least 1.5 to 2 times as deep as your turtle is long (so a 4 inch turtle should have a minimum depth of 6 inches). The length of the water area should be 4-5 times the length of the turtle, and the width should be at least 2-3 times the length of the turtle.

Between feeding and defecating, turtles are pretty messy creatures. A turtle tank should include a good filtration system such as a power filter or canister filter, or an undergravel filter system. Filtration will reduce the frequency of water changes, but your turtles will still require 25% water changes weekly and a thorough cleaning once a month or more. It is best to feed your turtle in a separate container to minimize the mess in the tank and reduce the load on the filtration system.

Heat
Water: 75-78 F (23-26 C), up to 80 F (27 C) for hatchlings
Air temperature: around 75-80 F (24-27 C) ambient air temperatures, with a basking spot at 85-90 F (29-32 C)

A submersible heater can be used to keep the water heated if necessary, but a broken heater is a potentially lethal situation. Protect the heater so the turtles can't bump it by placing it behind something (e.g. bricks) or by fashioning some sort of cover (a reader submitted this suggestion: place the heater inside a section of PVC pipe. Choose a piece with a diameter wider than the heater and a bit longer than the heater, and drill many holes in the sides of the pipe to allow water circulation past the heater). Get a good aquarium thermometer (not a stick on strip) and monitor the water temperature.

A heated basking spot should also be provided over the area where the turtle can get out of the water. An incandescent bulb or spotlight can serve this purpose, but make sure there is no way the turtle can touch the light or that the light can fall into the water. The basking light will help heat the air in the tank, and may also heat the water a bit.

Light
In addition to the basking light, a full spectrum reptile UVA/UVB light should be provided. Exposure to UVA/UVB is necessary for proper calcium metabolism, and also appears to have other benefits to overall health such as improving appetite. It is also nice to take your turtle out into natural sunlight in warmer weather. Get a proper reptile UVA/UVB bulb, and replace according to manufacturer's directions as the intensity of UV produced diminishes over time.