Every Civ may have exactly one Golden Age - often abbreviated "GA" - per game.
This lasts for 20 turns, and during those twenty turns:
- Every tile that produces at least 1 shield, produces +1 shield*
- Every tile that produces at least 1 commerce, produces +1 commerce*
* Both affected by Govt. penalties. E.g. in Despotism if a tile produces exactly 2 shields, +1 from GA is offset by -1 from Despotism penalty for 3+ tile production. This is why most players will try to avoid Despotic GAs.
Clearly this gives a significant boost to an empire's output; and the bigger the empire, the bigger the boost (particularly science and gold, not so much production as there may just be more overrun than before).
In all versions of Civ3 - Vanilla, PTW, and C3C - the way a GA is triggered is the same:
Either: Win a battle vs. another AI's unit (NOT a barbarian) with your Civ's Unique Unit
OR: Build a combination of Great Wonders whose traits cover your Civ's traits.
OR: Own (not necessarily through building, e.g. by capturing during a war) a combination of Great Wonders whose traits cover your Civ's traits, then complete a Great Wonder yourself.
The Wonder conditions can be somewhat confusing, so I'll give an example.
You are playing as France, who are Industrious and Commercial.
You build the Pyramids early on in the game. The traits of the Pyramids are Industrious and Religious (and Agricultural in C3C). So finishing the Pyramids alone is not enough to trigger a GA - you require a Commercial wonder as well.
Later in the game, you capture the Great Lighthouse from a rival. The Great Lighthouse covers the Commercial, Expansionst (an Seafaring in C3C) traits.
So now - you own two wonders whose traits cover your Civ's traits (Industrious from the Pyramids, Commercial from the Lighthouse). So you get a GA, right? WRONG. You didn't build the Lighthouse yourself. You have to build a wonder yourself to trigger a GA.
Now, later in the game, you build Sun Tzu's Art Of War. This is a Militaristic wonder. As you now own an Industrious and Commercial wonder, and you've just finished one yourself, your GA starts NOW. Note that the traits of the wonder you finish yourself, don't have to cover any of your own Civ's traits - as long as you own one or more wonders that do cover them.