Hardware
First tries with the RN4870U variant. Soldering can be tricky. So either using some sort of adaptor (I am not aware about existing adaptors for the RN4870 actually), or soldering very carefully with fine wire and a fine soldering tip.
Here soldered/connected:
- Pin 1 - GND (from MCU)
- Pin 2 - VBAT (3.3V) (from MCU)
- Pin 20 - UART_TX (to UART_RX MCU)
- Pin 21 - UART_RX (to UART_TX MCU)
- Pin 28 - P0_2/LED (to 100+240 Ohm resistors and red LED)
- Pin 30 - makeshift antenna
Baud rate e.g. 115200 (default); UART settings documented in the User's Guide, chapter 1.4.
BLE Scanner App
After the hardware has been set up the device and the peculiar BLE hierarchy should appear in the BLE Scanner App.
Screenshot on the right shows an already implemented private service UUID, beside the Transparent UART Service UUID.

Software implementation
It is basic ASCII command communication with a device capable of communicating on the serial port (e.g. Raspberry Pi), so I won't bother writing much about it.
E.g. in command mode (instigated with string "$$$") I can send "GNR\r" (or "GNR\r\n", doesn't matter) to the module, i.e. getting the name of the connected peer device. "V\r" would fetch the firmware version.
For my first tries I've been using an LCD to see responses that the BLE module sends back, and whether the data is plausible to begin with.