Testing with version 3.0.2 in 18.04.
Without having German or Italian support installed on my system I was able to switch to German and Italian, select them from the "Set language" setting (right-click outside text within document or under "Tools") and use spelling successfully.
Make default, press Enter.
It seems the OP already did that but then the spelling didn't work. That may be true or may be an impression coming from the fact that the setting above is somewhat buggy and the selection is not followed as expected, or rather the selection is a bit difficult to make - I had to repeat a few times in order to get the correct selection. It seemed to me that the "Make default" option is not immediately followed, in which case I made sure that my text intended for correction was selected, and then right-clicked while it was selected, and then chose "Set language", with double-click on the language name. To see which corrector is selected for different parts of text, click text and look at right-bottom of the Abiword window.
Maybe the 18.04 comes with installed aspell dictionaries that were lacking in previous ubuntu-s. And indeed, the instructions at the address linked in the question are partially outdated. There is no
/usr/local/share/AbiSuite-2.0/dictionary/ in the 3.x version. There is
/usr/share/abiword-3.0/ but without any dictionaries. I guess the 3.x program uses some dictionaries at system level, but I am not sure it's the aspell ones, because in Synaptic I only see
aspell-en installed (While German and Italian spellcheck is working without having those language added to the system).
In order to install aspell dictionaries they should be available in Synaptic or similar tools. In order to install them manually, go here, download the archive, open a terminal within the resulting directory and run
sudo make install
But that's not what made it work for me.