XDA is the living, breathing embodiment of the spirit of software engineering. At least, as applied to Android. And thanks to those fine folks, the inevitable march of progress has advanced yet again. XDA member BotsOne made two posts yesterday in which he confirmed that he and the others working on it were able to get read/write access to the system partition, and were subsequently able to install SuperSU.
That doesn't mean things are ready for the "average" root user (if there is such a thing). The developers that were able to achieve root on the S8+ haven't yet put their implementation together into a package for users, and allegedly they're still waiting on some files to get things working on the smaller Galaxy S8 as well. Even if you were feeling particularly adventurous, documentation for their current methods is a bit lacking.
When it does arrive, keep in mind that their current root method is exploit-based, so whatever security hole they're using is likely to be closed up pretty fast. That means the bootloader for the S8 and S8+ still hasn't been unlocked, which has its pros (KNOX isn't tripped) and some cons (no custom recovery, still can't ROM it).
I wouldn't be surprised to see their efforts hit public availability soon. The applicable thread on root progress for the Galaxy S8 and S8+ on XDA has exploded over the last day, pulling in a bit over 300 additional replies at the time of writing. But it's probably a good idea to leave the developers to their work, as it sounds like they're making fantastic progress.
- XDA Developers