Truly understanding this to the point where you are "caught up" with the field may take 2 years, but one of the big blessings of deep learning is abstraction. You can go from very high level "black box" approaches simply using and following example code from Torch, Theano, or Caffe, all the way to nitty gritty study of the details of various architectures, how to optimize them, and how to apply them.

Watching videos of presentations and reading slides is often much easier than comprehending papers, though ultimately the paper should have much richer detail.

Personal anecdote: Two years ago I just started learning about these things, coming from an undergraduate degree in electrical engineering. Now I am in graduate school for deep learning and AI working to push things forward, one small step at a time. It is totally possible to learn this stuff in a reasonable amount of study, and there are more free resources than ever. Note that I had a full time engineering job until 6 months ago... doing something totally different!