How do I start a console session with my $5 Cisco router through the RS-232 port?

I just acquired a cheap-o $5 Cisco 831 router with what would appear to be a custom configuration which does not allow me to access the router using "Cisco Router Web Setup (CRWS) software" via http://10.10.10.1 as described by Cisco's 831 documentation.

Searching for "console" and "connection" I found Connecting to the Console Port with Linux which is great, but the instructions are for a different router and do not apply to this unit.

And the rabbit hole goes deep after that. I found a manual, Cisco 800 Series Software Configuration Guide with over 500 pages of info. I looked for the obvious short goal, "reset" + "factory" + "defaults" and didn't find anything.

Help me get started, and please describe how to connect to the router via CLI/console session.

Connecting to a Cisco console port is pretty generic across all platforms with regards to the serial settings. The directions you found should point you in the right direction, but you may have to look up directions to connect to a serial console for your specific operating system and installed applications (you don't specify). Especially keep in mind that the specific reference to the serial port may be different on your OS and whether it is a true serial port or a USB-serial adapter.

As for the reset directions, here is the Cisco Password Recovery Procedure for the 831.

Good luck and welcome to the world of Cisco.