TL;DR: Learn some very basic linear algebra, learn Python, learn deep learning basics, learn a framework (PyTorch recommended), and start making stuff. Two full-time weeks are more than enough. Fast learner might make it in one week or less.

First you need to know some basic linear algebra. A deep understanding of it would provide you with deep insights into how deep learning works, but to start working with it, you only need to know the definitions of and basic operations on vectors, matrices, and tensors (they’re really trivial, don’t be scared by the names). I’m planning to write a blog post to introduce the very basics of linear algebra that you need to know, and will update this answer when it’s finished.

Then you need some programming skills. Python would be preferred, as it’s become the leading language in the field. If you already know programming but need to familiarize yourself with Python, I recommend this interactive course Learn Python on codecademy. It took me just like 2–3 hours on a Saturday afternoon to get started with that. You don’t need to pay attention to every detail. Sections like file I/O can be skimmed through or even skipped. You can always refer to the official Python doc whenever you encounter something new. I don’t really know how long it would take from scratch. My first language was Java, and I learned it before I know what functions and variables are in mathematics and what “while” meant in English, so obviously it took me long to get started with programming. But I guess for someone with better math and English backgrounds and starting with Python, it should much smoother.

After than you would need to learn some deep learning basics, like convolution, pooling, backpropagation, etc. Adit Deshpande from UCLA wrote an excellent series of blog posts introducing these ideas. Part 1 and Part 2 explained the basics of deep learning in very layman, very easily understood language. Part 3 listed some classical paper that represent major breakthroughs in deep learning since the ImageNet revolution (the start of this wave of deep learning explosion). The paper summaries are superbly written. If you are not going to do academics, then just reading the summaries instead of the original papers will give you a significant boost in your understanding of deep learning.

Finally, you probably want to learn a DL framework so that you can get your hands dirty. I highly recommend PyTorch. It’s so intuitive and native to Python that I learned it on a domestic flight. (Sorry you TensorFlow or other framework fans lol.)

Now, you are equipped to pick a task you’re interested in, say some classification or detection task. If you want to start your research, you can already find some latest papers for the task, reproduce them and, then and try to add your own ideas at this stage.