How to make a certain hat in a certain players inventory GUI to equip and wear?

Put a localscript in the button, put the hat in replicated storage and type the following.

!!Be sure to remove all hats on the player!!

local hat = game.ReplicatedStorage.Hat -- Change to hat name
local button = script.Parent

button.MouseButton1Click:Connect(function()
	local char = game.Players.LocalPlayer.Character
	if char ~= nil then
		local clone = hat:Clone()
		clone.Parent = char
		clone.Name = "Hat" -- Change to hat name
	end
end)

EDIT : if you want to make a equip and unequip, create a boolean value in the button and set it to false, then type the following

local hat = game.ReplicatedStorage.Hat -- Change to hat name
local button = script.Parent
local boolean = script.Parent.BooleanValue  --Change to the name of the value

button.MouseButton1Click:Connect(function()
	if boolean == false then
		local char = game.Players.LocalPlayer.Character
		if char ~= nil then
			local clone = hat:Clone()
			clone.Parent = char
			print("Equipped")
		end
		button.Text = "Unequip"
	else
		local char = game.Players.LocalPlayer.Character
		if char ~= nil then
			local clonedhat = char:WaitForChild("Hat") --Rename to hat name
			clonedhat:Destroy()
			print("Unequipped")
		end
		button.Text = "Equip"
	end
end)