Does the book cover how to get the position in the first place? I've read countless books (Like "The Managers Path" and "Managing Humans"), blog articles, etc, and tried many strategies, but it never seems to happen. Usually for the catch-22 reason of not having managing experience. I've even had past managers they had no worries about me having the skills or knowledge to do it... but it still doesn't happen.
If you have a good manager, they'll set you up for success, working with you to create a roadmap to get from IC to Manager. The steps in between would probably entail taking on larger projects, mentoring others, leading a project with multiple developers on it, and then after demonstrating all of that, you get the promotion.
In my experience, you get the promotion when you're already doing the job. In other words, you do the work and the promotion is recognition of the work you're already doing.
The other thing I'd say is that you don't get what you don't ask for. If you want to be a manager, ask for it. If you want more responsibility, ask for it. If you want better compensation or a new title, ask for it.
Unless you have a FANTASTIC manager, you will never just magically be recognized for your work. They will assume you're happy doing what you're doing and focus on greasing the squeaky wheel. To further your career, you should be a little squeaky. Ask for what you want. If you can't get it now, ask for help getting to that point.
I, as a manager, really appreciate it when someone gives me direction on what they want. Otherwise, I have to guess or try to pull it out of them, and I feel like I'm pulling teeth. It's hugely beneficial for a manager to have proactive direct reports. Be that person.
Good luck.