Uncalibrated monitors are lying bastards. An uncalibrated monitor might represent an image as being, say, less contrasty than it really is, or as having a color cast that it doesn't really have. Thus if you try to correct these problems by using some photo editing software, you might be making the real problems worse, or creating different or more serious problems. Color correction requires trusting your eye, but you can't trust your eye unless you can trust your monitor. Thus any money that you spend on digital image editing products for the purpose of color correction might as well be pissed down the drain if you don't calibrate your monitor. That's at best -- for often your images will look better untouched than if you modify them by reference to an uncalibrated monitor.
The solution requires getting a calibrator. The first step is to decide which one to buy.
Step 1: Choosing a Calibrator
As a rule, X-Rite products are slightly more expensive and tend to be slightly better. But I use a Datacolor product. The Datacolor Sypder3 was already out when I bought a used version of the Datacolor Spyder2 for $50 on ebay. It works very well.
Step 2: Using a Calibrator
You don't need to know how it works. But if you're curious, how it works is ingenious. By running through a series of shades of red, blue, green, and gray, the computer learns about the precise ways in which the monitor misrepresents the color data, and from this it figures out a way to outsmart the monitor in the future. In the future, it will lie to the monitor in such a way that the monitor's own lies will end up displaying the desired colors, so that the lies will all be canceled out in perfect fashion.
Step 3: Buy, Use, and Re-sell?
This solution is much better than not calibrating at all. However, professionals probably wouldn't do this, as a monitor's chemistry changes slightly over time, so that if one is being really picky then it is important to recalibrate on a regular basis: say, once a month.