Gamma
Move away from your monitor and squint your eyes. In the following test strip, the numbers 2.2 should almost disappear, meaning that you monitor is correctly calibrated to a Gamma value of 2.2. Careful: You will get different results in very light or very dark environments.
Another test: In the following strip the first two and the last two rectangles tend to blend into each other. If you actually see a difference, your monitor has perfect Gamma calibration.
Color depth and tone
Calibrating the color of your monitor with your eyes only is not possible. There are plenty of webpages on the internet, where you can download color charts and compare them to printed paper strips from KODAK or likewise. There are usually two types of color charts: RGB for monitors, beamers, websites, presentations and films, and CMYK for print products. You may also downlad Adobe Gamma, a tool which allows for some basic software-based calibration. If you're an image editing professional, you should buy a hardware-based monitor calibration tool.
If you have a good personal printer, and are generally satisfied with the printed results, you can also print out a photo (preferably showing human skin) or a color chart, hold it next to your monitor and adjust the colors until they match the printout. Make sure your monitor is in high color or 24-bit mode (Windows monitor & graphic properties), the room is dimmed, but not too dark, and there are no reflections on the monitor.
Never edit your images without a backup! (see Automatic Backup Option)
