What is the locations of the fonts that LibreOffice uses and how do install new and different fonts for the program to use?
Usually, fonts are manages by system tools like fontconfig. Thus, LibreOffice relies on those system tools in matters of which fonts are available. Just use your preferred package manager to add fonts from the ubuntu repositories, there should be a lot of TTF and other fonts available.
You can also install fonts manually, but that’s not a LibreOffice issue but a Ubuntu-related question. If you encounter problems installing fonts, Q&A sites like askubuntu may be the better choice to ask.
That being all corret - typically you can just drop your fonts to ~/.fonts - or double-click them in nautilus (gnome’s default file-manager) and (given that any font-viewer app is installed) click the “install” button in the font-viewer.
deleted -should’t be a wiki…
Clever idea… 
- but honestly: as currently almost none of the active users have sufficient karma to edit a wiki answer, it doesn’t make sense to set a question or answer as wiki - in contrary, with a lot of wiki answers, no one will receive enough karma to edit them. It would be “self-defeating” to do so…
This seems to be true for TrueType fonts but LibreOffice 3.6 is ignoring Type 1 fonts that are correctly installed with fontconfig and visible/correctly rendered by other applications.