I have three spys. Two are on Earth. Don't laugh but how do I send them to an enemy's planet? I have read through the espionage section so I must be missing something, again.
To assign a spy to an enemy planet, click on the enemy planet and then click on "Place Spy". You will then be able to place a spy on an enemy building.
You may also add a spy to your planet to increase counter-espionage. Spies assigned to your planets will slowly level up like any other citizen.
Spies assigned to races via global espionage screen will increase your knowledge of the enemy. At ultra level you may start stealing techs.
Unassigned spies show up in the civilization screen under counterespionage.