Videos
At this time, there's no specific documentation for QuantLib-Python, except for a series of screencasts that I started a while ago (you can find them on YouTube at https://www.youtube.com/playlist?list=PLu_PrO8j6XAvOAlZND9WUPwTHY_GYhJVr) but which is far from exhaustive; there's just a few of them for now, and there's no definite learning path.
However, the structure of the library in Python is the same as in C++, except for some changes (like the use of std::shared_ptr in C++ being hidden in Python) that were made so that one could write more idiomatic Python code. Therefore, you should be able to use the resources listed on the QuantLib site at http://quantlib.org/docs.shtml and translate their advice to the corresponding Python code.
One thing you might run into is that not all of QuantLib is exported to Python. Again, there's no documentation of what's there; so when in doubt, search for a feature inside the SWIG interface files to check if it's exported.
Update: last year, Goutham and I have pooled our material and published the QuantLib Python Cookbook. It's still a work in progress, but it might already be useful.
Further update: as of the end of 2024, A QuantLib Guide is also available.
You will find a tutorial of QuantLib using python with simple examples here:
http://gouthamanbalaraman.com/blog/quantlib-python-tutorials-with-examples.html
I have been writing these as a means to be instructive to others going through the process of learning and working with QuantLib. If you have suggestions on what topics you would like to read, please post a comment.