I actually just did this. Courses online such as Andrew Ng's Deep Learning course on Coursera and Standford course papers online are where I started. Then began working through tensor flow tutorials. Then looking up papers on modern neural net architectures. Took a matter or a few months to be productive. In the end, I realized that although neural nets are very fascinating, working on training them is tedious and not as fun as working on product code. I'd rather use the neural nets in a product, much like a sensor, than work on actually training the net.