Isolate what is attracting squirrels to your woodshed. Squirrels are attracted to food, so look for spilled birdseed or pet food that might be stored in your woodshed. Remove the source from the woodshed.
Examine the perimeter of the woodshed. Find out which part of the woodshed the squirrels are using as a point of entry. Cover any holes with wood or wire fencing.
Place live traps in and around your woodshed. Use sunflower seeds or peanut butter as bait. Release trapped squirrels in an area far away from your woodshed to prevent them from returning.
Apply squirrel repellent to your woodshed. There are several chemical solutions (Critter Ridder, Whole Control, etc.) available. Follow directions on the label and use only as needed.