The onboard degauss capabilities are usually quite good in modern computer monitors, but televisions, open frame monitors, and older computer monitors often need to be degaussed manually.
Pictures tubes have a metal screen inside called the shadow mask, which is designed to aid in focusing the color guns, and is supposed to negate the effects of the Earth's natural magnetic field. But the shadow mask itself can become magnetized, which can be the cause of many image problems.
Your display should automatically degauss itself whenever it is turned on. But it seems that modern PC monitors are the only ones that have really good onboard deguass capabilities. Televisions and other displays usually only have a weak onboard degauss that is not capable of handling major problems. For example, you can usually turn a computer monitor on its side, hit the deguass button, and have a perfect picture. That will not work with a television, try it with a TV and you will get image problems every time, even with a brand new set.
If your display has colors that change in different parts of the screen, appears washed out, has color blotches, or rainbows then it needs to be degaussed manually. Manually degaussing a screen can also usually fix damage caused by people with magnets.
To manually degauss a monitor you will need a tool called a Degaussing coil. They cost about $40 to $50 and don't require any skill to operate. To use one you simply turn it on, and move it towards the center of your screen. Then move it around in front of the screen in slowly widening circles until you are covering the whole screen. Then move it away from the screen while maintaining that circular movement. Turn it off, and you will be good to go. It is generally a good idea to degauss a screen whenever you move it, so make sure your screen is already where you want it before you start.
Degauss coils are available from many online vendors, and your local television repair shops may also carry them. They look like a round plastic hoop about a foot in diameter.