Espionage points (EP's) are built up slowly over time against all other nations. You can adjust the "weighting" of this so you can target particular civs if you like. You can then "spend" these EP's in spy missions. The cost depends on: the distance the target city is from your borders, the amount of trade you have with that city, whether that city has your religion, the length of time a spy has hidden undiscovered in the city, and the difference between your two EP totals. Note that this is slightly different for the counterespionage mission, and for the sabotage of map infrastructure. You can build up EP's more quickly (at the cost of science/income/culture) by using the slider. When deciding who to target, take into consideration the fact that when you defeat/wipe out a civilisation, all accumulated EP's against that civ are lost. Spies used to be quite powerful, but later patches have handcuffed them a bit. There is a lot more to espionage but it's more fun to find out for yourself