1. Overview of Color Correction

Color correction is something that Photoshop is particularly good at. This FAQ will give a simple overview of the different processes involved, and the tools available. Future FAQs will go into more detail. All the tools mentioned here can be found under the Image > Adjust(ments) menu item.

Before you begin
Color correction begins when you source the image. Although we don't always have the luxury of sourcing the image ourselves, given the opportunity, you should keep a few things in mind.

If you are taking a photo, be aware that the camera is not like the human eye. When you look at the sky during the day, your eye will adjust so that it's darker. When you take a photo during the day, you will often notice that the sky is brighter than you remember, usually lacking the same depth of color that your eye saw. That's because the camera was focussed on some other subject matter, probably much darker than the sky, so when a shutter speed was chosen, it was probably too slow for the sky.

There are many observations you can make like that. Having a good manual camera can allow you to experiment somewhat, maybe taking a picture that's too dark, just to see if you can retain some more detail. If you go too dark, all the shadows will become black and you won't be able to retrieve that detail. Go too light, and you'll have too much white in your image. The ideal is to have a broad range of detail from dark to light, without loosing anything at either end (sometimes called 'clipping'). To put it another way, a photo of a white cat in a snowstorm has a lot of detail that's nearly white, but if you take a photo that's too bright, you might loose some vital textures.

Basically, don't aim to get a perfect photo, but one in which all the detail is present. Then Photoshop has something it can work with.

Also, if it's possible to source your image with 16-bits per channel, then do so. Although only a limited number of tools work with this bit-depth, it can really help the initial color corrections, as it gives more information to work with. After that, you can switch back to 8-bits per channel and get on with the rest of your work.
Think Global
Now that you have your image in Photoshop, what's the first step to correcting color? Sometimes people look at an image and become too fixed on specific elements. That jumper is too red, the sky isn't blue enough, and so on. However, before you make any local corrections, you should always treat the bigger picture first. It's quite likely that specific flaws are part of a global problem, such as an overall color cast that just happens to be more noticable in one section.

Tone Correction
Before you correct color, you should consider correcting the tone. That is, making sure that the shadows are dark enough, the highlights are bright enough, and the midtones are suitable for the image. Photoshop provides three main tools for this task: Brightness/Contrast, Levels and Curves.

Brightness/Contrast no longer has a built in keyboard shortcut for it, probably for good reason. If you want to get professional results, it should really be avoided in favor of the other two tools. A future FAQ will explain the reasons in detail. Suffice to say, it's extremely difficult to use Brightness/Contrast without clipping some of your image and loosing some detail. Besides, anything it can achieve can be done better using the other tools.

Out of the other two, Levels isn't as versatile as Curves, but the histogram it uses makes it invaluable. If lots of data is converging on either the black or white point, you can probably assume that detail has been lost at those points.

The normal process using these tools is to set black & white points, followed by adjusting the midtones. In fact, this process can sometimes eliminate color casts too. Again, the details will be covered later.

Correcting Color
Using the eyedroppers in Levels and Curves can be a great way of getting rid of color casts. It also helps if you keep the Info palette open (Window > Info) so you can see the adjustments you're making. Start by identifying areas that should be neutral in your image (grays work best), as color casts are more likely to show up there. Shift click with the eyedropper tool (it will be automatically selected if you have Levels or Curves open), and you will have a sample point that shows up in your info window. If it doesn't display equal values of R,G and B, then you have some idea where the cast may be. Click that point with the 'gray' eyedropper to average those values out, and adjust the rest of the image accordingly.

Although the above will often be enough, sometimes the colors are still off. Maybe the 'neutral gray' wasn't supposed to be neutral, or maybe there are other colors in your image you would rather get right. One of the first tools many people turn to for correcting color is Color Balance. Although everything it can do can also be achieved using Levels and Curves, it does simplify certain tasks. It also shows you just how the colors interact with each other (eg. adding red will reduce cyan).

Hue/Saturation is another useful tool, especially because saturation is something that cannot easily be replicated anywhere else. This helps make colors more vibrant the more it's increased. Reducing the saturation can tone down an image, and checking the 'colorize' box can limit the color in your image to a specific hue - useful for sepia tone effects.

Conclusion
This FAQ was intended to introduce the concepts and tools required for color correction. It's not an exhaustive list, nor does it explain the techniques in any detail, but hopefully it gave you an idea of where to start. There are no hard and fast rules with color correction - after all, each image is different. I will be following this up with more detailed explanations of the different tools over the next few days.