Account age button is doing nothing, someone help?

First of all, we need to get the GUI button. Make sure your script is a LocalScript and put it inside of a GuiButton. For instance, the structure could look like this inside of StarterGui: ScreenGui > Frame > TextButton > LocalScript

Now to get this TextButton in the script:

local textButton = script.Parent -- The TextButton is the "Parent" of the script because it is above the script in the game hierarchy 

Now, since we're in a LocalScript, this script will be replicated to each individual player in the game. To understand this more I strongly recommend you read this. That being said, we can get the player like so:

local player = game.Players.LocalPlayer

Also, MouseButton1Click is not a player event, but a GuiButton event. To handle events, the syntax is as follows (where Instance would be something like Player or GuiButton):

Instance.Event:Connect(function()
	-- do what you want here
end)

In our case we would write:

textButton.MouseButton1Click:Connect(function()
	-- do what you want here
end)

Bringing everything together we get:

local player = game.Players.LocalPlayer
local textButton = script.Parent

textButton.MouseButton1Click:Connect(function()
	print(player.AccountAge)
end)

Hope this helped, and good luck!