I started learning it it last year. Here's my approach:
Read and took my time understanding the first eight or nine chapters of The Book. This took me around two weeks
I thought that gave me good enough foundation to begin a project so I started building one
I worked on the project for about six months. During that time, I revisited The Book multiple times to learn about different parts of Rust as I needed them. I also generously employed other resources like blogs and studying code from other Rust projects.
I'd say it took me about two months to feel productive working with it but way longer to feel confident about the code that I was writing. Actually no, I'm still not confident that my code looks anything like idiomatic Rust. Anyhow, I love Rust and it's now usually my first choice when considering a personal project.
TL;DR: Building projects and picking up things along the way as the project grows in complexity works best for me.