You primarily need a road to a city of the civ you want to trade with.
Here are two excerpts from the Civ3 site:
1st:
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How do I trade resources?
You can trade goods with another civ as long as you have a road, harbor, or
airport that connects your civilization with theirs. Once you have a trade route,
you simply negotiate with the other civilization in the diplomacy screen.
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2nd:
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Are there any requirements I need to fulfill before I can start conducting diplomacy?
Yes. To engage in diplomatic talks with another civ, you must first make
contact with that civ. You can do this either by physically entering their
territory or by trading another civ for contact with that civ. Other Civs may also
seek you out by entering your territory. You also need to establish an
embassy (granted by the writing technology) to be able to enter into
agreements more advanced than simple peace treaties. To be able to enter
into trade negotiations with other civs, you need a road connecting one of
your cities to one of their cities. To exchange world maps, you need the
technology of map making. Finally, you must be at peace with a Civ to tender
any proposal other than a peace treaty.
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So it looks like you need to have a road connecting you to the other civ, also need to establish an embassy (not sure if there is anything special needed to do that, doesn't look like anything more than Writing tech and contact with that civ)
Also, must be at peace with them.
[This message has been edited by canis lupis (edited August 23, 2001).]