The first on your list is a gun. Depending on what part of the year you are hunting and the particular strategy you use to hunt the squirrels should be the deciding factors in what type of gun to use. For example, early season, trees still have there leaves so shotgun with a heavier shot load is your best bet to reach out and touch those critters. Any shotgun size will do, but if you plan on eating the squirrel you may want to use a 20 or 410 gauge. If you want to try a real challenge use a .22 rifle. Also, you need to pick a decent shot shell load: 6,7, and 8’s are your best size load for squirrels.
Then the next squirrel hunting supplies are squirrel calls. Knight and Hale make a few that work pretty good. There are distress calls and there are regular calls for fox, gray, and red squirrels. Distress is probably your best bet and these calls are relatively cheap.
Don't forget that you'll probably need a good cleaning and skinning knife to go with your squirrel skinning accessories to process your squirrel/s.
See that wasn’t so much stuff. Equipment to hunt squirrels is inexpensive and it results into some pretty exciting action. The right gun, call, and ammo will definitely have a positive impact on your next hunt so invest in quality brands such as Remington, Winchester, Knight & Hale, Gerber, Buck, Browning, and Federal products.
Cabelas -
Great place to find squirrel skinning supplies and other gear for hunting those critters!
Bass Pro Shops -
Squirrel decoys, field dressing accessories, squirrel calls, scents, and other hunting gear to help get them squirrels.