Early fall squirrels is my favorite time of the year. If you get a good rain, it will usually cool off enough to make being the woods quite fun. It's still early enough, that you will almost certainly have the woods to yourself, and best of all, the squirrels are still uneducated to the dangers of humans hunting them.
Hunting squirrels is always about finding what they are feeding on. In the last summer/early fall, they are almost always feeding on hickory nuts. My brother and I went a few weeks ago, and we found one, and managed to shoot it, the next thing you know there wear at least 8 to 10 squirrels leaping everywhere around this tree, fleeing. It was the most fun we had had hunting in a long time.
While I prefer walking and making the squirrels move, another good strategy can be to find a good hickory tree, and sit off to the side with a .22 and pick them off one by one. With a good quiet .22, you can relax, and pick off quite a few squirrels in the same tree. This can also be great practice for larger game later in the season, and again, can be a great way to teach a child to hunt proficiently.