I must be stupid. I read the manual. I have the Intelligence Agency. Now what. The manual mentions clicking on the icon at the edge of the Info box. What are they talking about?? Help!
You could just double click the solid gray pentagon next to the name of the city which has the Intelligence Agency. Then you can plant spies. If it fails, don't try again for some x number of turns, I don't know what that number is, because it'll automatically fail again.
To use the spy, do as you do with an embassy - go to their capital, and double click on the pentagon.