The old glass television screens were easy to clean using glass cleaner and a rag, however plasma and LCD screens take a lot more care and can be easily damaged with chemicals and abrasives.  There are several ways of doing this.

Firstly, your television needs to be turned off so as not to damage the pixels as well as being able to see the screen more easily and more importantly the dirt and dust on it.

Use a microfiber cloth as it won’t leave lint behind and is also soft and won’t leave scratches.  Wipe gently over the screen to remove dust  and note it is really important that you don’t rub too hard as you will damage your screen.

Take a look at your screen to see if this cleaning exercise has been enough to get your screen clean.  If this is not the case and it is still grubby, dusty or has liquid splatters on it such as from sneezing, you will need to follow the next exercise.

Mix equal parts of white vinegar with water or use a specialist cleaning product for television screens.  Dab either solution onto a microfiber cloth and gently wipe the screen in circular motions, apply slight pressure to obstinate areas.  Never use harsh chemicals.  Afterwards dry with a clean microfiber cloth so as not to leave any streaks.