You've gotten a lot of good tips already. I'll share a couple of mine, which were passed down by my grandfather. He was always insistent that we get to the edge of the woods before daylight and we'd move into the woods a very short ways and then sit with backs to trees. Naturally, the woods I'm talking about were the woods where we already knew the squirrels would be. With luck, by first light there wouldn't be much wind. Any vigorously moving limbs were usually because there were squirrels either traveling or finding and munching acorns. If you can't shoot from where you are, move as quietly as possible to within shooting range. Unless you're great at sneaking, they'll spot you and lay on a limb until they think the danger is past. Grandpa and I would then sit down again, wait a short while and then he'd start flicking the small pebbles or acorns, that he'd gathered previously, into the dry leaves. That seemed to convince the squirrels that the danger was past and that other squirrels were feeding, and they'd come out then to get their share of the chow.
As for weaponry, he always used his Model 12 Winchester full choke and number 6 or 7 1/2 shot. These days, I'll use his shotgun or my Model 39A Marlin 22LR.