I know how to install TrueType fonts (by copying them to
/usr/share/fonts/truetype and doing
sudo fc-cache -f) but what about OTF formats?
I didn't find a suitable folder to copy them to.
The directory you're looking for is
/usr/share/fonts/opentype. If it's not there, you can just create it. Copy your OTF files there; this will install the font for all users. Then, recreate the fonts cache with the command
sudo fc-cache -f -v.
You can also install fonts per user at
~/.fonts/. It makes no difference whether they're in any sub-folders or what type they are. Mine, as an example, are organised by foundry.
Alternatively, you can just double click them, this will open them with the Font Viewer, which let's you install them with one click: