I work on a high frequency trading desk at a large bank. We do not use q for our trading models but just like the write of the parent comment, we use it for back testing / regression testing our models. Our quants also like writing / specifying the algo model in q and I or other developers would implement it in the language of our trading system.

IMHO, there are many resources for learning q on code.kx.com . I also went on a training course arranged by First Derivatives (they are the only vendor who offer formal training in q). I would say the best way of learning it is to practice! Use code.kx.com as a reference and download an evaluation copy of the runtime. You should be able to find open source / Free editors for q (QInsightPad, there is also an Eclipse plugin). Set up your environment and try to tackle the Project Euler question set in q.

Alternatively, get a linear algebra / machine learning text book and attempt to solve the exercises in q.

q may seem a little terse, but it is extremely expressive and once you get the hang of the syntax and error handling, it is a joy to use.