To build a RESTful API using Spring Boot for a project, I would start by creating a Spring Boot application with the necessary dependencies for web support. I would then define controller classes annotated with @RestController to handle HTTP requests. 

Each method in the controller would be mapped to specific URLs using the @RequestMapping or @GetMapping, @PostMapping, @PutMapping, and @DeleteMapping annotations. The controller methods would process requests, interact with the service layer, and return responses in JSON or XML format.