Foundation:
Start with (re)learning math. Take those boring university level full length courses in calculus, linear algebra, and probability/statistics. No, unless you're a fresh STEM graduate, 10 page math refreshers won't do. If you're self-studying, make sure you do all exercises and take practice exams to test yourself.
Tools:
1. (Re)learn C/C++, as well as a linear algebra library, such as Numpy or MATLAB. You will also have to learn parallel and distributed programming at some point (CUDA, MPI, OpenMP, etc). Next take a boring university level full length course on algorithms and data structures.
2. Get a book describing ML algorithms, and implement them yourself, first using plain C, then with MPI or CUDA, and finally using plain Numpy/MATLAB, or one of the low-level ML frameworks (Theano or TensorFlow).
Application:
Finally, start doing ML. Not learning about it, doing it. Choose an application that interests you (computer vision, NLP, speech recognition, etc), and start learning what you need to make something work). Focus on specific, practical tasks. If you don't have any particular application in mind, go to Kaggle, choose a competition, and read what models/tricks the winners used. Then jump right in and start competing.
The first two requirements might take years to master, but if you skip them, you won't be able to do any serious work in ML, or even understand latest papers. You will be a script kiddie, not a hacker.