Colors cannot be wrong in the viewfinder on any DSLR which includes the Rebel T3i. This is simple physics in that light coming in through the lens is reflected to the viewfinder, so what you see is simply the light that is there. The only way that would not be the case is if you have a colored-filter attached to your lens.

When a picture is taken, the camera by default produces an image based on its Picture Style, Image Parameters applied to the current style and White-Balance. If you are seeing wrong colors every time, you probably screwed with those settings and I advise you Reset your camera from the setup menu. This will bring it to a default sensible state which should give reasonable output under general use.

For what is still wrong, you probably have a problem of Automatic White-Balance. This happens mostly under indoor lighting and when you have scenes dominated by certain colors. Outdoors should rarely be a problem. For example, if you shoot inside and your walls are brightly colored, the camera can give you really weird results. The easiest way to make this better is to select a WB Preset according to the type of lighting you have: Tungsten, Fluorescent, Shade (if not artificial lights are on), etc.

To get white-balance perfect you need to use the camera's Custom White-Balance function with a white-balance card (or other accessory) which is basically an object which is known to be perfectly white. The camera takes a measurement from that and you get colors looking well-balanced. You can even get decent results by using a plain white-sheet of paper.

When you got the camera reset and WB good, you can adjust the Picture Styles to your liking. There are a few styles to start from Standard, Vivid, Natural, etc (the exact list depends on your camera) and each can be adjusted in terms of Saturation, Contrast and possible other parameters (depending on the camera model).

For the exact buttons to press, please refer to the manual which came with your camera. Some camera come with a miniature paper manual in which case you will find the full manual on CD/DVD. Look-up the terms I mentioned and it will be clearly explained.