How can I make the Raspberry Pi and BeagleBone Black talk via serial?
The BeagleBone Black has 3.3V logic level signals. Its serial ports are all 3.3V ports. UART0 is tied to the debug header, and is hard coded for the debug log from the BBB. It is not useful for standard communication between two devices.

You have two main options. Luckily, the BBB has multiple UARTs that can be enabled. Turn one of the other UARTs on and connect the appropriate pins from the expansion headers to the RPI. Since the RPI defaults to a UART shell on the serial port, you can ssh into your BBB and then use minicom or similar to talk to the RPI from there.

Alternatively, you can use a USB serial cable on the BBB's USB Host port (or OTG if you needed to). AND you can also do the same on the RPI (so you have two usb to serial cables connected together), but that would require some setup on the RPI, a catch 22.