"In the LO that's on my machine, there is no "Fields" (or hyperlink) on the Insert menu"

For reference, I was looking at the Word processor on LibreOffice 3.4.0 OOO340m1 (Build:12) according to help->about. It's the Linux version I looked at just now, but I'm used to using the Windows version and they mostly behave the same way, certainly for straightforward menu selections like that.

So it's strange that you aren't seeing an "insert field" function.