Rust's approach to asynchronous programming involves using async/await syntax similar to JavaScript, but with a key difference: Rust requires the selection of a runtime to execute asynchronous code. Runtimes like Tokio and async_std are essential for handling async operations, as Rust does not include a built-in runtime, offering flexibility but requiring more setup. The guide provides a practical walkthrough on using async in Rust, illustrating how to start a runtime, spawn futures, and manage CPU-intensive tasks without blocking the executor. It emphasizes the importance of choosing the right runtime and enabling necessary features in the Cargo.toml file. The tutorial demonstrates the concurrent execution of tasks using Tokio, highlights the differences between async functions and blocks, and provides examples of handling web requests and combining CPU-intensive tasks with asynchronous operations. Overall, the guide aims to simplify the process of writing async code in Rust while introducing essential concepts and best practices for beginners.