What are the best resources available online for learning design thinking?

Design can only be learned by doing.

The Stanford d.school has a Virtual Crash Course at http://dschool.stanford.edu/dgift/ that takes you quickly through the process with a partner--design is also best done in teams.

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UPDATE 5/9/16: IDEO U has paid courses on ideou.com taught by some of their heavy hitters.

UPDATE 4/15: Coursera is currently running a class: "Design: Creation of Artifacts in Society" starting April 29, from Karl Ulrich at UPenn/Wharton. He's also published a free e-book you can use with or without the course: http://ulrichbook.org

Also on Coursera: Human-Computer Interaction from Stanford's Scott Klemmer, started March 31.The material is geared towards making user interfaces, but the design thinking process is simply a generalization of the design process, which Klemmer uses throughout in the context of UI. Recommended!
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After every project, no matter how small, ask yourself: "How did the process work for me? Where do I feel confident? Weak? Excited? Anxious?" Then iterate and improve yourself. Don't judge yourself too harshly. If you aren't failing, you aren't doing it right. But remember: design is supposed to be playful and fun.

After that, try using the d.school "mixtapes" (more in-depth) http://dschool.stanford.edu/dgif... with another quickie design project. Ask for design project challenge ideas on Quora.

Then study the Bootcamp Bootleg: http://dschool.stanford.edu/use-..., and do another quickie design project. Attempt to use more of the tools. Also see the IDEO Human Centered Design toolkit [used for social enterprises and NGOs.]

Find someone else interested in learning with you, and use something like Edistorm to brainstorm with them, and Evernote to keep track of your interview notes and design insights and ideas.

Finally, find someone who can mentor you online. I don't know of a comprehensive course, so the best option is to get someone with experience to coach you through it. [I just started doing this for a friend.]

And then... do a few more design projects! Get involved with OpenIDEO. Make boring things fun. Think big and start small. And let us know how it goes!