Two of the most productive ways to hunt squirrels are still-hunting and stand hunting.

Still-hunting
Walk slowly through the woods, stop often and watch for movement in the treetops.
Stand hunting
Sit near a nut tree that squirrels are cutting and wait.
Squirrel dogs
Treeing dogs find squirrels and bark until the hunter arrives. Hunting with dogs has grown in popularity.
A great first hunt
Squirrel hunting does not require total silence or stillness, making it a great hunt for new and young hunters.