Question: I've noticed an increasing number of jobs that are asking for experience with data mining and business intelligence technologies. This sounds like an incredibly broad topic but where would one go if they wanted to develop at least a partial understanding of this stuff if it were to come up in an interview?

Answer: 
A very good book with practical examples is the  

[Programming Collective Intelligence: Building Smart Web 2.0 Applications](https://rads.stackoverflow.com/amzn/click/com/0596529325) by Toby Segaran.
Consider reading [Ralph Kimball's books](http://www.amazon.com/s/ref=nb_ss?url=search-alias%3Daps&field-keywords=ralph+kimball&x=0&y=0) for an introduction to Business Intelligence.
Also, try to not stick to one technolgy-vendor, every company has its own biased vision of BI, you'll need a 360 overview.