Some Chromebooks do, some others will and many never will. See the list of Chromebooks with Linux app support for a basic (current) list.
If you’re a developer, you might be able to set your Chromebook in ‘developer mode’ to run your own Linux apps.
Be aware that (currently) Linux desktops e.g., Unity or XFCE, are not supported.
You don’t do anything for this support. The Chromebook either supports it or it doesn’t. You might need to update your OS.