For those that are still new to the scientific Python ecosystem, we highly recommend the Python Scientific Lecture Notes. This will help you find your footing a bit and will definitely improve your scikit-learn experience. A basic understanding of NumPy arrays is recommended to make the most of scikit-learn.
There are several online tutorials available which are geared toward specific subject areas:
An introduction to scikit-learn Part I and Part II at Scipy 2013 by Gael Varoquaux, Jake Vanderplas and Olivier Grisel. Notebooks on github.
Introduction to scikit-learn by Gael Varoquaux at ICML 2010
A three minute video from a very early stage of scikit-learn, explaining the basic idea and approach we are following.
Introduction to statistical learning with scikit-learn by Gael Varoquaux at SciPy 2011
An extensive tutorial, consisting of four sessions of one hour. The tutorial covers the basics of machine learning, many algorithms and how to apply them using scikit-learn.
Statistical Learning for Text Classification with scikit-learn and NLTK (and slides) by Olivier Grisel at PyCon 2011
Thirty minute introduction to text classification. Explains how to use NLTK and scikit-learn to solve real-world text classification tasks and compares against cloud-based solutions.
Introduction to Interactive Predictive Analytics in Python with scikit-learn by Olivier Grisel at PyCon 2012
3-hours long introduction to prediction tasks using scikit-learn.
scikit-learn - Machine Learning in Python by Jake Vanderplas at the 2012 PyData workshop at Google
Interactive demonstration of some scikit-learn features. 75 minutes.
scikit-learn tutorial by Jake Vanderplas at PyData NYC 2012
Presentation using the online tutorial, 45 minutes.