Before anything else, watch this 3 minute video that shows through a 3D model how the deep learning process works:
https://www.youtube.com/watch?v=3JQ3hYko51Y
If you want to get a little bit more into the nitty gritty, there is no better than 3blue1brown's intro:
Part 1) https://www.youtube.com/watch?v=aircAruvnKk
Part 2) https://www.youtube.com/watch?v=IHZwWFHWa-w
Part 3) https://www.youtube.com/watch?v=Ilg3gGewQ5U
How to get your head around the idea of machine intelligence? By far the best way to do that is to read this wonderful piece of "what if" technology fiction. Really, do it.
http://www.goodreads.com/book/show/6665847-daemon
Jason's machine learning blog is good reference, but not strictly focused on just deep learning:
http://machinelearningmastery.com/blog/
And a couple of different courses you can look into:
https://www.udacity.com/course/deep-learning--ud730
This ones goes more in to using python and building your own neural nets as opposed to just using a library such as Keras:
https://www.datacamp.com/courses/deep-learning-in-python
Andrew Ng's Course on Deep Learning
https://www.coursera.org/specializations/deep-learning
It's kind of important to at least know what's going on the hardware size, for example Google's Tensor Processing Unit:
https://www.blog.google/topics/google-cloud/google-cloud-offer-tpus-machine-learning/
A far more established eco-system is Nvidia's GPU productline specifically related with deep learning and their developer program might be a good place to start learning more about it:
https://developer.nvidia.com/deep-learning
Then of course the rapid prototyping platform for machine intelligence ideas (even for non-programmers):
For a couple of years now we've maintained a blog that try looking at these topics from a theoretical standpoint rather than practical (as everyone else seems to be doing):
Machine Learning Yerning
Deep Learning on Python
https://www.manning.com/books/deep-learning-with-python
MIT Deep Learning Book (in pdf)
https://github.com/HFTrader/DeepLearningBook/blob/master/DeepLearningBook.pdf