Rust is very different in other languages. In many languages, implementing data structures is easy, and so it's how you start out. In Rust, it's not easy. But luckily, you don't have to write them yourself! That's what crates.io is for. Or, if you want a basic linked list, there's one in the standard library.

That said, linked lists are almost never what you want anyway, so it's not particularly relevant to most Rust programmers. And when you do, you use one of the ones that have already been implemented and move on with life.

The "Too many linked lists" book linked from the post goes into this in great detail.