OK, initially downloaded the TGZ files from here and expanded the folder; ran the program via the SweetHome3D shell script in the SH3D folder.

That obviously didn't work for me, so I nuked that folder, and the downloaded TGZs, and installed via the Ubuntu Software Centre. That install refuses to even show a splash screen.

Uninstalled that, and I'm now re-downloading the TGZ files and giving them another go.

First up the 64 bit version: I choose RUN or RUN IN TERMINAL - nothing happens. (I've got a dual core 64 bit AMD box)