1. Find "Program Files\Infogrames Interactive\Civilization III\Text\Civilopedia.txt"
2. Open it up in a text editor.
3. Find a similar entry (like "Democracy" if you're adding Fundamentalism").
4. Copy and paste the old entry somewhere in the same general area (it rarely matters where).
5. Change out all the info and save.
Voila!
The document itself explains its syntax at the top, so I won't write it, here. Suffice it to say that there are a couple "custom" tags, like "Description" that serve special purposes, but most of it is straight text.
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