[blululu]

The answer to this question depends on your level of computer & math proficiency. Some folks here have been debating about the relative merits of practice vs. theoretical foundations, but this dispute makes some assumptions about where you are starting from and where you are most comfortable. The fastest way to learn something is to fit it into a framework that you already understand. If you have a PhD in theoretical physics/abstract mathematics (like a lot of ML researchers), then the more mathematical (theoretical) frameworks will be a good way to build deep intuitions. If, on the other hand, you are more into applied data analysis, then you will probably find that working on applications will be the easiest way to go.

Personally, I enjoyed both Andrew Ng's and Geoffrey Hinton's respective courses on ML and Neural Networks on Coursera. You may also want to check out Michael Neilsen's online essay on deep learning (http://neuralnetworksanddeeplearning.com). Ultimately I would also encourage you to supplement your understanding by applying this work to your own applications. The universe is often the best teacher.