@adam-worth What Chromebook do you have? You may need an ARM build, or an x86 build depending on which you’ve actually got.
The short version is that you need to activate Legacy boot mode, which will allow you to boot from a USB. From there, installation is as you would any Linux distro on any computer. I’ve been running Linux on my Acer C720 chromebook for years (it’s a Haswell i3 with 4GB of RAM, with an after-purchase upgrade to a 120GB M.2 SSD). How to enable Legacy boot mode varies based on what Chromebook you have, but it’s usually some hotkey you have to hold at startup to enter dev mode, followed by a command to configure it at console in Chrome OS. Legacy Boot Mode uses Coreboot to boot the laptop, and should work with any modern distro.
The Arch wiki has done a pretty good job of writing up what kind of support there is. https://wiki.archlinux.org/index.php/Chrome_OS_devices
I’d suggest booting from a live USB and testing everything first, to make sure you aren’t going to run into hardware issues - when I first installed Linux on my Chromebook, it needed a weird touchpad driver that wasn’t in mainline kernel yet. I was able to work around it with an X configuration, so it wasn’t a deal breaker, but be aware you might have to do stuff like that.
Stop reading here if you aren’t prepared to irrevocably destroy your Chromebook in a way that would prevent it from booting at all.
On mine, I installed a 3rd party BIOS from johnlewis.ie. It wasn’t necessary to the function of the laptop, but it got rid of the Google Chrome logo on startup and a prompt that delayed boot by a few seconds. I would not advise installing it until you’re absolutely certain you’re never going back, and are ok with the prospect of possibly bricking it to the degree that you’ll have to tear it down and replace the motherboard. I never had a problem with mine, but your mileage may vary.