You can send Spies to asteroids of other players, which you found in your radar or by random Pirate raids.
You need to have free at least one slot of Aggression.
Espionage mission duration depend of the distance between asteroids, but anyway in 3 times faster then attack mission. The exception is pirate raids with fixed duration time.
You'll see information of enemy's asteroid according to your Access level:
0 - you see nothing - alived spies back to your asteroid
1 - you see Buildings on asteroid
2- you see also Resources, Generals and Starbase
3- you see also Observer - top panel
4 - you see also Secondary asteroids
If you gain access level 4, the victim won't know who exactly spied him.
You can also purchase a premium service - Boost of espionage or Autoespionage aliens.