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If you want to be extra fancy, you can falconry hunt them. It is probably best to use a red tailed hawk or some other buteo species, as their hunting style is best suited for this. They prefer to fly up to a tree then sit and wait while you scare up game, then chase and strike. They'll follow you above, flying from tree to tree, as you advance, beating on bushes and branches with a stick. The goal is to try to bring squirrels up from the ground and into the trees where they are easy quarry for a bird of prey. Once they're treed, it is game over for the squirrel as they have to plan every one of their movements from limb to limb to avoid plummeting to their death, but an aerial assault requires no such hindrance aside from a swift dodge here and there.
The real challenge in squirrel hunting is that with a rifle or shotgun, the squirrels know to make it difficult for you to get line-of-sight so you don't have an opportunity to shoot them. This is where the term "playing squirrel" comes from. When it comes to hunting with a hawk, if they aren't physically holed up deep in some hard structure, they're effectively out in the open and completely exposed, period. Hawks will even reach into squirrel nests with their talons and yank them out and drag them to the ground. Shit is animal planet.