Just right click on youre city containing the wonder that allow spys, then you will get the option of doing some things (depend on how advanced you are.)
I dont remember exaktly been some weeks since last time i have played.
On the intelligence wonder's city, an icon for the agency will appear after building it, in the position where the capital city's icon is. Just click on that to try to insert spies in AI capitals. Once spies are successfully inserted, espionage can begin.