How to connect an Elegoo Nano to a Raspberry Pi and program it?
The Elegoo website has a downloads page which contains the drivers.


Using the Raspberry Pi, download the zip file containing the drivers.
Unzip the contents to a location of your choice. (Also see here)
Change to the directory containing the Linux driver source files (ie CH341SER_LINUX).
In the terminal type make. Let it compile the driver.
In the terminal type make load. 


Done