While I am not a big fan of the current DA spy system, I have figured out a few tips and tricks to make it usefull. Under the Dread Lords spy system you just set your sliders on the first notch as early as possible and forgot about them.
The Dark Avatar system is obviously very different. On the other hand it is not as obvious how to use it in a efficient manner. Others have discussed what to target to use spies offensively, but I am going to concentrait on how to use them to gather info.
The first thing to note is that the magic number of spies is 3. If you have three spies or more in a given civ, you will gain information quickly. If you have 1-2 you gain info very slowly. I reccomend NOT sending any spies to any civ unless you can send 3 or more at a time.
The second thing I noted is to only keep you spies in any one civ until you have the moderate level of info on them. At this level you can get the full report of what techs they have and you can check their ships to see where they are going. In the early stages of the game this is 99% of the info that you want anyway. Getting this leve is easy and should only take you 5 turns to gain with 3 or more spies. After you have moderate info on everyone, then you can go back and shoot for higher levels where you find it necessary.
The last thing I have noted is to never hord spies for defence. I was one who was appauled at usuing my spies to cripple civs who had done nothing to me, so I just built up my spy levels to what I thought was an impenatrable defence (around 20.) This seemed to work out well as although I was being constantly attacked, no one could get through the sheer numbers I had. Then I got the 'every planet in the galaxy gets their own spy' event. I was playing in a gigantic galaxy and had over 250 worlds in my empire! Needless to say I never got rid of all of them and they were a constant thorn in my side. Because of the interactive way that mega-events work, the more spies you have, the more likely you are to get this event.
I have given up on using spies to actually steal techs. I have never found a consistant way to do this, so I have relagated it to the catagory of the occasional random bonus and not something you can work toward.
Scincerely,
Scintor