There are three parts to this and two ways of making it. I tend to use the eastern Greek/Middle eastern method, but my ex-mother-in-law's filling recipe.
The three parts are:
pastry (a packet of filo pastry)
nut filling
syrup (see below)
The filling is made from a mixture of nuts. Almonds always, though the western greeks tend to favour walnuts as the second nut, and the further east you go the more likely it is that pistachios or sometimes cashews will make an appearance. Some of the less reputable shops use breadcrumbs to make the filling cheaper, but it doesn't taste anywhere near as nice.
My prefered filling is two cups each of unblanched almonds and walnuts, a cup of sugar and half a teaspoon of ground cinamon. Put all ingredients into a food processor and zap it till the almonds are fairly well chopped up. If you dont' have a food processor or are phobic about electrical appliances, you can chop the nuts or put them through a nut mill or grater, then mix it up in a bowl.
When the filling is prepared to your satisfaction, you can begin constructing the baklava in one of two ways. The flatter middle-eastern style baklava (the one most people know from shops because it's much easier to do in large quantities) is done by lining a buttered baking dish with a sheet of filo pastry, brush it with butter, add another sheet, brush with butter again, then continue this way until aproximately half of the pastry has been used. Spread the nut filling over, then continue with the remaining sheets of pastry, again brushing with butter. Brush the top with butter and pour the remaining butter over. Score through the top few sheets of filo in diamond, or triangle shapes to mark the serving pieces. (Actually I've just remembered a third way I've seen done on occasion, where the layers of buttered filo are each sprinkled with the filling mixture. Think the lady responsible was Cypriot but can't be sure.)
The other method is to make baklava rolls. Place a sheet of filo pastry on the bench and brush it with butter. Sprinkle it with the filling mixture and roll across the long side of the pastry. Tuck the ends under and place the rolls thus formed side by side in a baking dish.
However you've chosen to construct your baklava, bake it in a moderate oven until the pasty is golden.
Make a syrup using 2 cups sugar, 2 cups water, about 1 tbsp lemon juice, a strip of lemon rind, small piece of cinnamon stick, and a few cloves. Boil for ten minutes.
According to the greek ladies of my aquaintance, the secret with the syrup is to either have both the baklava and the syrup hot, or both cold. Pour the syrup over the baklava (strain it or you will be picking bits and pieces off for ages). Cut into serving pieces and serve at room temperature.
Baklava rolls are traditionally cut on an angle to give a piece which is diamond shaped when viewed from above.