How would I make a frame visible when you hold a tool and when you put the tool back it's invisible?

This can be achieved by using two events which would be Tool.Equipped and Tool.Unequipped.

By using these events you can detect when a player equips a specific tool and when they unequip that tool.

Insert a Local Script into your tool and use the following code:

local Tool = script.Parent
local Player = game.Players.LocalPlayer

Tool.Equipped:Connect(function()
	-- Here you will need to locate the frame you want to make visible.
	Player.PlayerGui.ScreenGui.Frame.Visible = true
end)

Tool.Unequipped:Connect(function()
	Player.PlayerGui.ScreenGui.Frame.Visible = false
end)

Links: Tool.Equipped, Tool.Unequipped

Hope this helps.