it's... easier than you might think? about half of them are relatively mnemonic and most of the others are close to a mnemonic (∩ is on 'c' but ∪ is on 'v'). If your on linux you can say set the windows key to shift over to an APL key binding (it's always present in KDE, in gnome enter
gsettings set org.gnome.libgnomekbd.desktop load-extra-items true at a terminal then it will show up in the input menu)
and both Dyalog (free now for non-commercial use) and GNU APL (via Emacs) have secondary input methods until you get comfortable.