The best research results from 2014 and 2013 make less use of the unsupervised techniques than initially expected, so I would start by focusing on the below sections, which focus more on supervised learning with deep neural networks:
Sparse Autoencoder: Neural Networks, Backpropagation Algorithm
Building Deep Networks for Classification: Deep Networks: Overview, Fine-tuning Stacked AEs
Working with Large Images: Feature extraction using convolution
You'll need some background in matrix algebra, calculus, and probability to understand this. Having taken a previous machine learning course, although not strictly necessary, is probably extremely helpful--I'd recommend taking any standard course on ML on Coursera or Udacity, or going through any standard textbook.
EDIT: I almost forgot that Michael Nielsen (who wrote the standard textbook on quantum computation) is also writing a free online textbook on Neural Networks and Deep Learning. Chapters 1-4 are currently available and would get you pretty far: http://neuralnetworksanddeeplearning.com/