The best methods to place spies is to:
A) Place in mass amounts. This gets large amounts of spy man-weeks done at a time before the AI can react AS well. If you trickle in 1 every time you gain one, so will they. Mass amounts I consider 10+, you really need to swarm them.
Aim at any facility that generates increased income. Spies are created off a slider that goes from 0%-25% of your income. If you decrease their income amount, you decrease the amount spent on training a spy, thus slowing the training process. A spy has a solid bc cost designated to it (depending on how many you've trained so far that game, it goes up as you train more and more, thus my 10,000bc comment).
Once those two things are taken care of, if you get to the point that you can pop out a spy faster than they can (due to your increased espionage ability and hopefully stronger economy) then you can continually keep them locked down and eventually even spread more spies into their worlds.
It's a slow and COSTLY endeavor, often cheaper to just buy armadas worth of ships and troop carriers. BUT I've been able to pull the lead man down to attackable range by shutting his economy down, thus restricting his navy. Once I had him running in the red, his ships started disappearing due to wars and never were replaced.
Most cases though I'll just place about 4 or 5 to a race just to hit Low rating to see their influence ratio number, then pull them off from that race. After that I'll place them on planets I'm about to conquer to shut down morale (for propaganda invasion) or farms (to starve billions of people the week prior to invading).
