Python as you already know is a programming language that is included in default installations of ArcGIS. There are many ways that you can learn how to use this language, some free and some not. I have put together a list of some training resources below:
ESRI has web tutorials geared for Python use in ArcGIS.
You have to have/create an ESRI account to gain access to their educational files above.
Once you have mastered the basics of Python and would like to learn about ESRI’s arcpy package, you can use the Python window in ArcGIS 10 to explore the calls. The window will give you hints on how to complete commands. The best way to really learn Python is to experiment and make mistakes.
If you are using ESRI products, use Model Builder to develop your work flows, export the model to python and you will have perfect ArcPy representation of the model. This isn’t Python exactly, but if you are using Python, getting to know ArcPy and Model Builder will help tie all of the pieces nicely together.