Excellent thread going here. I have hunted squirrels for over 50 years...not a great hunter, but you do learn a few things in that length of time.
Went out this morning with two grandsons and two fiest dogs. Had a fun time even as warm as it was. Only killed three squirrels, but that's why they call it hunting. And we did have a good hunt! The dogs treed at least ten times and the squirrels hid out. We had to shake a lot of vines and beat on old den trees to get them to make a run for it. Nothing like a scared gray squirrel to test your marksmanship.
Early in the year when there are lots of leaves on the trees I usually hunt without dogs. Like the man said, find a good bunch of oak trees down in the bottom, sit quietly, when the squirrel moves shoot him or stalk until he is within range and then shoot. Sit quietly after the squirrel drops because often others are nearby. This is fun hunting but not as much fun as hunting this time of year, and on up to February after the leaves are fallen. After the leaves are gone you do much better with a dog.
Dogs smell where the squirrel has been on the ground and trail him to the last tree he went up. Then the dog barks and you need to run to him before the squirrel timbers from tree to tree and escapes. By the time you arrive at the tree the squirrel will either be hiding in that tree or a nearby tree. You just walk around the tree(s) and look for part of a squirrel peeking at you from a fork of the trunk or some big limb.
Really lots of fun! Let me suggest a site:
www.sqdog.com Click on books and magazines and order "Squirrel Dog Basics". It will give you a world of information on squirrel hunting with a dog and still hunting.
Good luck!