How to provide standard library sources for IntelliJ IDEA's Rust project?

As commented, the supported approach is to use rustup:

• Navigate to https://rustup.rs/ and follow the installation instructions for your platform.
• Add the rust-src component by running: rustup component add rust-src
• Create a new Rust project in IntelliJ and choose your existing Rust project source. If the folder already contains previous IntelliJ project files, you may have to delete those first before it will let you proceed.
• IntelliJ-Rust should automatically configure the standard library sources to point to the sources downloaded by rustup.

As a reference, since the question title is broad, for Fedora 28 I had to:

dnf install cargo rust-src
sudo ln -s /usr/lib/rustlib/src /usr/lib/rustlib/x86_64-unknown-linux-gnu/

then give /usr/lib/rustlib/x86_64-unknown-linux-gnu/src/rust/src as "Standard library"

Full setup:

Issue opened to simplify the process

Although the preferred way of installing Rust is by using rustup, as pointed out by the other posts, it is not uncommon to use the packages that your distro makes available.

I use, for example, the packages provided by Gentoo and I share the same problem about the not prefilled field for standard libraries. Nevertheless, you can easily find out where your standard libraries have been installed by typing the following find command:

find /usr/lib* -type d -name "rust" | grep src

or the following if you installed rust in your home

find  -type d -name "rust" | grep src

The previous commands will help, unless, of course, in your distro there is a package for the binaries and one for the source and you only installed the binary one.