I believe the way to clean an LCD TV screen would be the same as cleaning an LCD computer monitor. There are many who recommend using a solution made up of 50% isopropyl alcohol and 50% water. More on that
here.
I use distilled water only. This is applied to a fresh handkerchief using just enough to make part of the material damp. This is applied gently to the screen to avoid damage to the panel and to prevent the dirt itself causing scratches. A dry part of the handkerchief is then used to wipe the dampened screen dry, again using gentle pressure only.
I find most marks will eventually come off using this method. It would be easier to use two handkerchiefs, one damp and one dry. However, using only one helps to keep the laundry down
