How is the avionics/system software installed? do they install it in the avionics bay using CDs or floppy disks?

Windows Update.

Probably via data uplink I could imagine. But definitely interesting to know.

Floppies  

Or a usb stick on modern aircraft.

- Floopy disks on older aircrafts.

- CD and floopy on actual aircrafts via a PC connected to a dedicated plug.

I think the good old floppy disks, cd are used to update the navdata at each airac

I don’t know how the fms and other onboard software are updated: I guess they change an electronic card in the avionic bay ??

We use USB sticks for honeywell and steam machines  for universal( well the last time I did anyway)! 

you mean you use usb stick to update which software of the a320?

In the AHD Helicopters we use SD Cards for mostly everything, sometimes ARINC datalink for configurations or stuff like that. Could imagine that they use similar things on the modern airliners