Espionage is reached through the main diplomacy window (the first tab). Click on a leader portrait, and underneath of their image on the lefthand part of the window you will see an espionage slider. Put that slider to a greater than zero amount and you'll begin spending money on eventually gettting access to their information.
When you reach a point that you can access more information about the civ, you'll get a message telling you so. If you want to increase your knowledge faster, add more to that slider. After you reach "ADVANCED" levels of espionage with a race, increased spending allows you to steal technologies from them.