There isn’t really a Euclidean mode as such, instead it’s just another mathematical function (or OP / operator in Teletype terminology) that you may mix up with any other code.
The video at the top is me using the pattern editor as a poor persons interface to a “scene” that’s based on Euclidean rhythms.
Your best bet is to start with the Teletype documentation on the Monome website. Unfortunately they’re a little bit out of date as the firmware is now at version 2.0. But if you work your way through them you should get to the point where you can begin to understand how to use the
It’s also worth having a look through the new docs, you can get them in the 2.0 firmware zip file, but these currently have no introduction to using the Teletype, so they might be a bit challenging until you know what you are doing.