module object has no attribute 'Screen'

Adam Bernier's answer is probably correct. It looks like you have a file called turtle.py that Python is picking up before the one that came with your Python installation.

To track down these problems:

% python
Python 2.7.1 (r271:86832, Jan 29 2011, 13:30:16) 
[GCC 4.2.1 (Apple Inc. build 5664)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
>>> import sys
>>> sys.path
[...] # Your ${PYTHONPATH}
>>> import turtle
>>> turtle.__file__
'/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/lib-tk/turtle.pyc' # Should be under your Python installation.
>>> 

If you see something like this:

>>> import turtle
>>> turtle.__file__
'turtle.py'

Then you'll want to move turtle.py (and any corresponding turtle.pyc or turtle.pyo files) in your current working directory out of the way.

As per the comments below, you'll find a wealth of information about a module, including its pathname and contents by calling help() upon it. For example:

>>> import turtle
>>> help(turtle)

Rename turtle.py. It is clashing with the imported module of the same name.

I tested that the code from that site works in Python 2.6 (without installing any external packages).

From http://docs.python.org/tutorial/modules.html#the-module-search-path

When a module named spam is imported, the interpreter searches for a file named spam.py in the current directory, and then in the list of directories specified by the environment variable PYTHONPATH.

So the Python interpreter is finding your turtle.py file, but not seeing a Screen class within that file.

Johnsyweb's answer contains several good tips on how to debug this kind of issue. Perhaps the most direct way of determining where on the filesystem an imported module resides is to use repr(module) or simply type the module name at the REPL prompt, e.g.:

>>> turtle
<module 'turtle' from '/usr/lib/python2.6/lib-tk/turtle.pyc'>