Typically, a green hue is caused either by a setting in the TV's menu, or through a loose or damaged wire between the source and the TV. This problem can usually be resolved by making a few minor adjustments.
To determine what exactly is causing the green appearance, first check whether it happens on other components. If the green is still there when watching cable, while playing games or while watching movies, it is likely a settings option. Bring up the Menu, and navigate to Color Settings. This effect is often caused by the saturation setting, so adjusting that can eliminate the problem. Most TVs also have the option to reset settings to default, which may be an even easier fix.
If the green appearance only happens with one component, this suggests that something is amiss with the wiring connecting that component to the TV. Ensure that a solid connection is made to the component and to the television. If this is the case and the green appearance persists, follow the cable all the way between the TV and the component looking for any fraying or other damage. If there is a damage, replace the cable. Most component cables are sold in the electronics department in stores. However, some may require calling the component's manufacturer.