The easiest way to get started with Rust without needing any local installation is to use the Rust Playground. It is a minimal development front-end that runs in the Web browser and allows writing and running Rust code.
The execution environment of the Rust Playground has some limitations, such as total compilation/execution time, memory and networking so another option that does not require installing Rust would be to use a dev container, such as the one provided in the repository https://github.com/microsoft/vscode-remote-try-rust. Like Rust Playground, the dev container can be run directly in a Web browser using GitHub Codespaces or locally using Visual Studio Code.
For a complete local installation of Rust compiler and its development tools, see the Installation section of the Getting Started chapter in the The Rust Programming Language book, or the Install page at rust-lang.org.