I've improved a lot at squirrels this season. So far I've not come back empty handed. Of course, I've just jinxed my next trip for sure! I hunt alone with a scoped .22 and don't use dogs. I rely on their natural curiosity and aggressive behavior to bring them to me.
I think the advice given in this thread varies greatly with the area of the country you're in and the type of squirrel you're after.
Colorado mountain squirrels will use the same tree for what appears to be years judging by the pile of pine cones and cuttings. I've found looking down and listening is more important than looking up. Look for signs of feeding on the ground around tree trunks or the sound of them barking. When I find one of these trees I get myself into a safe shooting position (considering the missed or pass through shot) and sit and wait. You can train your eye to notice the signature movements of squirrels, be it a flick of a tail, any horizontal movement, or how the branches move differently to the wind. Spotting their shape even in the shadows is getting easier now as well.
If it's the middle of the day the squirrels are not so active but, because of the feeding piles, I know they're around. So discharging a round usually wakes them up and they come out mightily angry. I might try to mimic their bark by kind of clicking my tongue off the roof of my mouth. They usually start barking and you can home in on their position. If you have to move to get a shot, move slower than normal, but you don't have to crawl. Just slow deliberate movements, and that includes your hands and head. Circle the tree rather than approach it and move away to get round obstacles. I've been surprised how much movement they tolerate.
If they spook and run, they likely run down the backside of the tree and away from you put of sight. In the middle of the day I might sit and wait and see if after 20-30 mins they come out, but towards the end of the day there's usually a more active one close by, so I move on. In CO they are very territorial, there is rarely more than one squirrel per tree. The estimate is one per acre, but I've found that in some areas, it's often slightly better than that.
Now the snow is in the high country, it's easier to see recent activity. The piles of cones and cuttings are still visible right now but there is often new cutting on the snow. Fallen logs are road ways and in areas of high traffic. I've had some luck sitting and watching the busy paths to see them move around. They again, are great indicators to let you know this is a good place to set up and wait.
The squirrels in Colorado spend a surprising amount of time on the ground, running from tree to tree. Their dark bodies stand out against the snow. When I find areas of high ground traffic I get high over and open area and watch the ground for movements, then move slowly into position. I don't try for the shot while they move but knowing which tree they're in is enough to close in on the hunt.
Even if there is a lot of cutting or sign on the ground, if the trees are too thick for a clean shot, you can be frustrated by hearing them bark but not be able to locate them. After that happens a few times you can begin to recognize the areas that are worth your time, and no matter how much sign, the trees that will house the old men of the woods, while they laugh and even throw pine cones at you.
Regardless of the success rate, I've found squirrel hunting a great way to get into the hills and back to natural ways. It was also great preparation for my first deer hunt this year, I didn't come home empty handed from that hunt either.
