At last success, and with batteries too, rather than taking power from the computer, so I can soon start sewing!
One stumbling block was that I got an error:
avrdude: error: USBtiny_transmit
It turns out that I needed to upload the code to the Gemma while its bootloader was working (i.e. the red light was still on).
avr doesn’t stand for anything apparently. It’s just a particular kind of chip used in the ATiny microcontroller from the Atmel Company.
avrdude is a command-line program for programming AVR chips. I assume that means it’s similar to the commands I put in the LX Terminal with my Raspberry Pi.
Well, happy making and tinkering in 2016 everyone!