I just dived into some of Udacity's data science classes and it's very easy to get started with numpy. I'm just scratching the surface but it still feels amazingly powerful. Pandas is another great tool that goes hand in hand with data, its like Excel inside your Python REPL with SQL tools and more.

Online class is one way to start, another would be picking a dataset and a goal for it and diving in. Kaggle.com has a number of content projects and a great deal of past data science stuff that's open sourced, I've been browsing it for ideas and approaches. Another source of inspiration might be local open data initiatives, your city, county, or state might have a pile of data available for interesting projects.

I think half the battle, at least for me, is not deep statistics or other maths skills, it is just diving in and trying stuff.