In my experience (as someone who enjoys both reading and writing) it's generally a question of demonstrating the concrete value of reading and producing written artifacts. I tend to start with teaching people how to write because it provides the most tangible outcomes: an outline, a plan, a draft, or a memo. When you're able to coach someone into expressing a raw idea of theirs as words on a page, the value of writing becomes clear very quickly.
From there, it's a matter of them warming up to the notion that internalizing the writing of others works in the opposite direction. Once they understand that reading and writing is the process of serializing and deserializing mental models (and that the result of this process is lossy at best, and actively misleading at worst), that's when the switch flips from "casual" to "critical" reader, and "amateur" to "practiced" writer, in my opinion.