Just go to the local car parts shop and get yourself a bottle of Autoglym red and gold wax. First apply red (you really don't need that much), let sit a while until it gets dried, then buff. This wax also cleans, but if the playfield is really dirty, You need something else to get the grime off of it before waxing.

When done, use the gold labeled Autoglym. This one is almost watery-like so let it soak in the rag and then spread all over playfield. It dries for quite a while; in most cases about 15 minutes is enough. When completely dried, buff with a very clean antistatic rag and have a beer. Or two beers.