Here's the bare minimum you'll need to become productive using Python for scientific computing.
This is Python's official home, where you'll find the current version of Python, documentation (in English, with some documentation in many other languages), and links to a wide variety of 3rd-party resources.
The Python core language, though powerful, is simple in the sense of offering only a minimal amount of built-in functions. You provide additional functionality by writing your own Python scripts or modules, or by importing already existing modules. Python comes with a Standard Library of modules implementing a large amount of commonly needed functionality, such as access to system calls, string manipulations, basic math functions, etc.. If what you need isn't in the Standard Library, check the Vaults, a categorized and searchable index to 3rd-party Python resources.
This very active and helpful Usenet newsgroup is the place to go to get quick help from experts on issues not covered in the documentation. It is also where you'll find the latest news on Python developments, including announcements of new modules and discussion of upcoming enhancements to Python. Other sources of personalized expert support are the Special Interest Groups (SIGs). These groups maintain email discussion lists (archived on the web) devoted to such topics as MacOS platform-specific issues, Python in education, plotting and graphing, and image processing.
A handy summary of the Python language and several of the most-used library modules. Available in HTML (including a downloadable zip file of the whole site), plain text, and PDF. For printing, consider the less up-to-date TCC quick reference listed below, formatted more suitably for hardcopy.
From this page at Python.org you'll likely find a version of Python for your platform; use the latest version (2.2 as of Dec 2001) if it is available for your platform. In addition, there is a Python implementation written in Java--Jython--which will allow you to use Python on any machine with a Java implementation. Jython gives you full access to Java's GUI capability, but will not be able to run "standard" Python (aka CPython) code that uses Python extensions written in C, C++, or FORTRAN (this includes some useful numerical extensions, though the JNumeric package addresses this limitation to some degree).
UNIX/Linux/Solaris users note: You will likely be installing Python by compiling it from the source files via the standard "config/make" command sequence (though Linux users may find a suitable RPM for installing binaries directly, and some Linux distributions include a version of Python). Some very useful libraries must be installed before you install Python if you would like to use them: the Tcl/Tk libraries and the PIL (Python Imaging Library) core library. Python comes with a very nice integrated development environment (editor/debugger) called IDLE that relies on the Tcl/Tk GUI package to implement its GUI elements; you will need a Tcl/Tk installation in order to use IDLE. PIL is a Python package that lets you create and manipulate images in a variety of formats. For it to be compatible with images in Tcl/Tk format, you must install Tcl/Tk and compile PIL's library before you install Python. However, PIL can be used without Tcl/Tk, so you needn't install Tcl/Tk if you don't plan on using IDLE or on manipulating images in Tcl/Tk format. Astronomers who are using NASA's FTOOLS package will likely have a version of Tcl/Tk already installed that they can use for building Python with Tcl/Tk capability.
The most important 3rd-party package for scientific computing is the Numeric package, known more colloquially as "NumPy" or "numpy." Python's built-in numerical capability is adequate for simple tasks, but is too slow for large-scale computing. NumPy is a package of Python modules and extensions that gives Python sophisticated array computational capability with performance close to that of raw C or FORTRAN code. If you are on a UNIX-type platform (e.g., Linux, BSD, Solaris), you will need to download and install NumPy via this link. Windows users will find a precompiled version of NumPy at the Windows download page. The MacOS version of Python comes with NumPy already installed.
These three documents are part of the official documentation; they are available in many formats (HTML, PDF, PostScript, etc.). I strongly suggest you print them and bind them for quick reference. Here's what you'll find in each document:
The Python Tutorial by Python's inventor, Guido van Rossum, provides a quick but surprisingly thorough introduction to Python. There are many quick introductions to Python, but van Rossum's is the best I've yet come across for physical scientists already familiar with computing. You may also want to browse some of the other tutorials listed on the Introductor Material page at Python.org.
The Python Library Reference documents the large number of modules that come with the standard distribution. For scientific computing, the most-used information is in the first five chapters (though chapter 8 on "The Python Profiler" will also be useful). Print just these chapters; keep an electronic version of the whole reference handy in case you need other chapters. The first chapter documents important elements of Python's built-in capability; you should at least skim this chapter soon after you familiarize yourself with Python. Then skim the table of contents so you'll know where to find other information as the need arises.
The Python Language Reference provides a terse technical description of the language. It is not as useful as the other core documents and you needn't even crack its cover to start being productive with Python. But it will occassionally come in handy to help you understand some details of the language. In particular, in the likely event that you find yourself doing object-oriented programming with Python, you will find its coverage of "Special method names" handy to help you make your custom Python classes implement standard behaviors.
Another handy summary of the Python language and several of the most-used library modules, produced by the New Mexico Tech Comuter Center. Available in PostScript and PDF. It may not cover the most recent version of Python, but is still very useful.
The documentation for the Numeric package is available both as a printable PDF file and as HTML for online viewing. Terse, but it will get you there.