Into the woods as quietly as you can, preferable before sunrise, full camo is best. I cannot stress how much more sucessful you will be if camo'd out. Ive had squirrels cross into a tree above me, see this mass of something underneath it, and come down within feet of me trying to figure out what I am.
Find mixed hardwoods, preferably in creek bottoms, but any good mixed hardwood area is good. Areas with taller trees good place to start if no creekbottom. Find a place to sit and get comfortable. If Im going to a new area I am prepared to sit for at least 30 minutes watching for any movement. Most of the time squirrels will forget about you in 15-20 minutes if you are camo'ed and motionless. If nothing after 45 minutes then I am ready to quietly ease up and quietly and slowly move to new areas and repeat.
The closest thing I have found to a sure bet in unfamiliar mixed hardwood bottoms is a tree that has fallen across a creek. For some reason tree rats love to run horizontal timber. The next best thing is to find a point on a creek where two trees come together close enough that they can use to cross. This is especially good if that is the only place to cross a creek for a good distance either way.
Bellows calls tend to work in areas with fox squirrels. I will wait 15 minutes after sitting and tap out a soft bark pattern. Greys and foxes bark differently, sound different, and have different rythem. Sometimes the call will bring younger squirrels to me, curious about a new voice in the woods. Generally, though, the sound of the call seems to put them at ease and gets them moving again if they are around. If no response, then I bark out another time after about 25 minutes. Ive not had much luck with greys and calling though.
Dont be offended, because I dont know how much you know, but make sure you know what squrrel barks sound like. If you are moving though the woods and hear squirrels sounding off, you are moving too fast/noisily. Grey squirrels also give out an alarm shreik.
Next year when the leaves are up, a good hunter will find the squirrels with his ears and stalk it. Another good way is to sit still and watch for limb movement that isnt in line with breezes. It is easier to stalk up on a squirrel cutting feeding in a tree with leaves. You cant see it and it cant see you. Your advantage is that you can see the limbs moving so you KNOW its there. After the leaves fall squirrels will spend most of their time on the ground.
Squirrels rarely travel alone. If you see one and are camo'd out, sometimes it pays to just sit and watch and see if there are any more bringing up the rear.
I use a scoped 22. I dont think there is anything to beat it while hunting tree rats. 22 noise seems to not spook all the squirrels in the woods. Ive even shot, missed, and shot again while a squirrel did little more that perk its ears up before returning to cutting an acorn. Shoot a 12 gauge and many times you will shut down the forest for at least 30 minutes. If you are hunting greys, they are smaller and move more, stopping only for less than a second every so often. Hunting greys with a 22 will force you to become familiar with your gun, good trigger habits, etc.
Good luck and if you try of my suggestions, let me know what works for you and what doesnt.