In DL, you fund espionage at the bottom of each races picture in the foreign relations screen; the portion where you can scroll sideways to see all your contacted races. Eventually that money builds up to Low, Medium, High, and Advanced levels of knowledge of that civ. You can't get more knowledge of planets, attitudes with spending beyond Advanced, but sometimes you may get stolen techs.
In DA, it is totally different. You fund espionage at the bottom of the economics screen, for the whole civ. This money eventually buys you an agent (or multiple agents). You'll get an announcement, and an icon on the stack at the right of the main screen. Using the espionage tab of the economics screen, you can either place the agent on a developed square of an opponents planet, or you can place the agent on an enemy agent on one of your own planets, nullifying that enemy agent. A third option is just to save up agents for awhile, so you can saturate a rival's planet later with several agents that won't all get nullified quickly
Agents in place on rival planets have 2 effects. One: as long as they are in place, you build up your general knowledge of that race, as in DL, to Low, Medium, High, Advanced, and occasionally steal techs when you have them thoroughly scoped out. Sometimes, if the target civ is quick at nulifying agents, it may take the successive efforts of several brave agents to build up to a change in your knowledge of the target civ. Two: an agent in place stops all the functions of the planetary improvement it is placed upon, until nullified; this means, for instance, no income multiplier from an Economics Capital that is being sabotaged.
drrider