Pistachios ripen in the month of September almost exclusively around the world with the exception of Australia which harvests in February. In exceptionally hot summers, harvest may be early (last week of August).
How to tell when the pistachios are ripe
The hull of the pistachio is called the epicarp. It is about 1/16 of an inch thick and adheres tightly to the hard inner shell until the nut is ripe. Take your thumb and forefinger and squeeze the nut. If the epicarp has separated from the hard inner shell, the epicarp will easily come apart and can be peeled off.
Besides the epicarp coming off easily, the color also changes. The epicarp has a reddish/yellow color during development. The color lightens in August and when ripe, it is a rosy, light yellow.
Try to time harvest when most of the nuts are ripe.

The pistachios will fall off the tree when the branches are given a sharp shake. A rubber mallet hitting a branch, a fist or mechanical shaker can be used. Put sheets or tarps under the tree to catch the nuts. You don’t want to nuts to fall in the dirt (you will lose them or the epicarp will tear).

Should you desire to salt the nuts, make a super saturated solution of salt and water (stir in salt until the water is so full of dissolved salt, it will no longer absorb any more and the salt you add doesn’t go into the solution). Dip the nuts in the solution. Remove and return to the drying table or put in oven to roast. Use a low oven (225° F) for 15 to 20 minutes.

Pistachios keep very well if just a few precautions are taken. In general, the lower the temperature, the longer the storage life of the nuts. Pistachios can be held at temperatures up to 68° F without significant quality deterioration for as long as one year. Prolonged heat turns the oil in any nut rancid. A cool cabinet, the refrigerator or freezer are all good storage locations.