How to break into machine learning

An engineer recently asked me how she could turn an interest in machine learning into a full-time job. This can be a daunting prospect, because the whole field has until recently been very separate from traditional engineering, with only a few specialists at large companies using it in production, often far from traditional product teams. I took a very random path to focusing on deep learning full time, but so did most of the people I work with. It's not clear that there is one good route, but I wanted to share the advice I had to offer in case it's helpful to others. Every manager should point at one member of their team and say "You are now our machine learning expert".