First, get the windows clean. Nothing and I mean nothing works better than crumpled up newspaper with your favorite glass cleaner. Use one sheet to apply and work the cleaner around the window and another to dry it, especially if the film is heavy. Try it and you'll be amazed at how good it works. No colored print, just the black and white newsprint. And you can't beat the price!
Once you have all the oils off the window, watch how long it takes to accumulate. It's normal to have body oils, plastic ougassing etc leave a film over the course of a month or two. If it appears before then and there is no environmental reason for it, you may have to look at slow leaks in your heater core as one example.