The DVD is good for those new to window cleaning, I'm intending to do a review of it, as is Tosh.
Damp cloth - dry cloth is fine, many swear by it.
Better in my personal opinion is to use a proprietary window cleaning spray.
Use Tesco's own brand, about 79p for 500ml.
Very lightly, and I mean VERY lighty mist a few panes and use your dry microfibre to buff clean.
As you are a newbie then you will need a couple of microfibre cloths.
The windows you are describing are called Georgian by the way.
Now if the windows are stinking dirty you will have your work cut out, you can even be better off using a bucket and sponge ( with hardly any detergent in the water)
Wash the whole window, frames and all, can be a sponge or just take the sleeve off your applicator and use that, use loads of water and do a whole load of the windows too.
You might even have to change your water a couple of times.
When they have dried off a little (you will have got most of the water off with a wet cloth) go back use either a sprayer and mist & buff or use the wet scrim - dry scrim method.
The above is really a method for cleaning a pig pen of a clean, I don't know why I explained it, but I've never so far on the forum seen a description of how to clean a real pig pen clean trad style on georgian windows...I've too much time on my hands obviously
Ian