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)