If you want to avoid the math (not my personal recommendation), I would start there and just mess around. Build small things and start reading more as you get comfortable. Its definitely an area I would encourage learning in an iterative way: try to learn a small amount, try and apply it, repeat.
For the Neural Network type stuff we used in this work, I would recommend Michael Nielsen's awesome website as a starting point http://neuralnetworksanddeeplearning.com/ and keras https://keras.io/ is the easiest NN library to pick up and get something going with. Andrew Ng's mooc https://www.coursera.org/learn/machine-learning is also a good starting point for some slightly more general machine learning background.
If you want to avoid the math (not my personal recommendation), I would start there and just mess around. Build small things and start reading more as you get comfortable. Its definitely an area I would encourage learning in an iterative way: try to learn a small amount, try and apply it, repeat.