How to update Xcode Command Line Tools?

For future travelers, here's a version-agnostic approach. First, run softwareupdate --list. This will probably take a couple of minutes. When it's done, you'll see a bulleted (with an asterisk) output like this:

$ softwareupdate --list
Software Update Tool

Finding available software
Software Update found the following new or updated software:
   * Command Line Tools (macOS High Sierra version 10.13) for Xcode-10.1
        Command Line Tools (macOS High Sierra version 10.13) for Xcode (10.1), 190584K [recommended]

Find the bullet that refers to the Xcode command line tools. Copy that entire line (except the asterisk...). In the above case, you would copy: Command Line Tools (macOS High Sierra version 10.13) for Xcode-10.1

Then, run the install command (as shown by Brendan Shanks) with what you copied inside quotes:

softwareupdate -i "Command Line Tools (macOS High Sierra version 10.13) for Xcode-10.1"

Run softwareupdate -i "Command Line Tools (macOS El Capitan version 10.11) for Xcode-8.2". The quotes are important.

I'm going to answer a slightly different question here, because this question came up when I searched for a solution to my problem. Hopefully it'll help someone (and it'll surely help me next time I run into the same issue).

I wanted to upgrade the command line tools from version 8 to 9. The App Store didn't suggest this upgrade, and neither did softwareupdate --list.

xcode-select --install

installed the new version of the tools. But clang --version still gave 8.0.0 as the version number. xcode-select -r and rebooting didn't solve this issue.

xcode-select -p returned /Applications/Xcode.app/Contents/Developer, and clang --version reported an installation directory under there. I thought I'd start over again.

sudo rm -rf /Applications/Xcode.app

deleted version 8 of the tools. But xcode-select --install said the command line tools were already installed.

sudo xcode-select -r

Now, sudo xcode-select -p returns /Library/Developer/CommandLineTools/.

It seems that the problem was that the new version of the tools are installed to a different directory, and xcode-select -r is not clever enough to find the latest version.