hehz0r - if your solo hunting, I recommend doing a lot of sitting still and watching rather than hiking through the woods hoping to spot some movement. Both ways work, but I've had the best luck sitting at the base of a tree trunk as still as possible. If that particular spot isn't productive after 5-15 minutes, I move on. Sometimes I stay longer, sometimes less.
If a squirrel is runs around to the other side of the tree there's no sense in chasing it; you'll be doing laps for a good while. Instead, while you're standing on the other side, grab a rock or branch with your trigger hand (this is the least cumbersome way for me). Shoulder your rifle, and then under-hand toss the object on the other side of the tree where the squirrel is hiding. This usually makes the squirrel run around to your side where you can get a decent shot.
If you wish to learn to clean a squirrel,
click here. That link leads to a a multitude of ways to clean squirrel.
One tip I'll give you is to keep the squirrel wet as possible while you skin it. This will help keep hair from getting onto the meat (which can be a pain to remove).
When I clean squirrel, I do so outside with my hose running. I constantly water the squirrel down through out the process. Before I make any cut at all, I drench the squirrel down while massaging it from head to toe in order to get it as wet as possible, and to wash away any loose hair or other debris.
Good luck, be safe, and have fun.