How to make a text button that creates another text button?

You need to use the Instance.new function in order to create ROBLOX Objects (or Instances) from Lua code. Aftering 'Instancing' it, you can code its properties and listen to its events like any other ROBLOX Object:

local button = script.Parent
local newButton = nil

button.MouseButton1Click:connect(function()
	if newButton then newButton:Destroy() end

	local random = math.floor(math.random()*100)

	newButton = Instance.new("TextButton")
	newButton.Size = UDim2.new(0, 500, 0, 250)
	newButton.Text = "Another example of setting a property"
	newButton.Parent = script.Parent.Parent

	newButton.MouseButton1Click:connect(function()
		print("New Button Clicked! " .. random)
	end)

end)