Although you can actually do the cleaning while the television is off, it is best to turn it off. There are spray cleaners that are available in the market that are safe to be used. Again, check first with your manufacturer, to be safe. Make sure to use lint free cloth whenever possible to erase marks that are left on the screen.
You will be surprised how becoming your tv set will be after your regular maintenance. As for the plasma stand, you can use a dedicated cleaner, like a wood furniture conditioner, for stands made of wood. When you choose to use a damp cloth on the stand, make sure to follow it up with a dry cloth.