Scrum Delivery – How do you coordinate activities to go from user story into implemented code?

Apologies if this is a stupid question – I've just begun learning about Scrum and feel like I'm getting a handle on the project management side, but it's still unclear to me how the developer team moves from user stories to implemented code, and I can't seem to find any materials that address this!

User stories are written from the standpoint of high-level user functionality and may require technical changes in bits throughout the entire solution. A waterfall approach would involve progressing from high-level user story-like requirements to detailed technical requirements that a developer can implement. What does this look like in a scrum?

Let's say I have a user story; I'm sure I can't just throw it at a developer and expect them to implement it; they'd need a design? Is it their responsibility to create the design, or does a lead software engineer collaborate with them?