Where can Scripts/LocalScripts run?

Well, I've had a bit of an issue lately.

I've written a little script that should be running, but it's not.

I'll try to explain what's happening briefly, as some of this may or may not be relevant: I have a server script in Workspace that clones a bunch of folders, parented to one folder into the player. In this group of folders there is a localscript with this simple code:

wait(1)
script.Parent.DescendantAdded:connect(function(new)
	print("Added ")
end)

that should run when I insert something from ServerStorage into the folders.

Here's what the folders look like, for a better idea: http://gyazo.com/e53b1df071d997f0efa348f2220eff90

I've tried this in localscripts, scripts, and I've tried some different events, but it seemed more like the scripts just aren't running. So I'm wondering, why is my script not working? Can localscripts and/or scripts only be ran from certain places?

Thanks for reading, I know it's very trivial but it would help a ton if we could figure out a solution to this. I feel like I might be messing up something painfully obvious, aha.

ServerScripts can work in game.Workspace, game.ServerScriptService, a Player's backpack, a Player's PlayerGui, and game.ReplicatedFirst. LocalScripts can be used in these parts, but run on the client side. I like to use LocalScripts to get the player (game.Players.LocalPlayer) and to get the mouse of the player (game.Players.LocalPlayer:GetMouse()). LocalScripts can also run inside a player's character. I hope this helped!