Fluorescent bulbs cast green light across everything around them.
Light is the center of a photographer's skill, and yet, also the bane of his existence. Light means everything to a photo; the strength and color of light can add a warm rich tone to the image, or it can overpower the subject and completely ruin the picture. Therefore, a photographer must know that indoor fluorescent bulbs cast an ugly, sickly green color across everything around them.
Autopilot
The easiest way to handle the problem of shooting under a fluorescent light is to simply allow the camera to deal with it. Most digital cameras have an option for adjusting the White Balance, and many even handle it automatically. This setting allows the camera to compensate for any color cast in the resulting pictures. Changing the White Balance setting to "Indoor" or "Fluorescent" tells the camera to account for the extra green light added to the scene by the ambient light.
Filter It Away
Film cameras are a bit harder to work with, because they can't automatically compensate. The proper technique is to add a counter-color to the photo by mounting a filter in front of the lens. Because fluorescent lights supply extra green and less red, the best results come from a red filter. Don't forget to compensate for the filter by letting more light into the camera; the red filter makes pictures darker, so open the lens wider to account for it.
Flash Power
Sometimes the green light can be overpowered with a flash. Set the camera to slow-sync mode. The camera holds open the lens longer than usual, allowing the background to expose properly, and then it fires the flash to properly light the subject. This is the same technique used for portraits against sunsets or cityscapes. The background---which isn't lit by the flash---carries the green color from the fluorescent lighting, but the subject is lit by the flash.
Shooting in RAW
Newer, higher-end digital cameras shoot in RAW mode. This is less of an image format (like JPG or BMP), and more of a data format; think of it as the basic ones and zeros stored by the camera when the photo is taken. The advantage of RAW mode is that the White Balance has not been applied to the images. The disadvantage, though, is that the photographer must apply the White Balance to each of those images, so the trade off is loss of time for complete control of the color adjustment. Many photo editing programs (such as Photoshop) have a RAW editing feature.
Fix it in POST
Sometimes, there's just nothing that can be done at the scene. Perhaps the camera doesn't have a proper White Balance setting, or it doesn't compensate enough. When the photographs come home, load them into your favorite photo-editing software and experiment. Just like shooting RAW, each picture requires an adjustment. Keep in mind that the fluorescent lighting add excess green, so either reduce green or add red to counter it.