Now there are several strategic ways to use spies, and since it’s a new game element, my advice here may not be perfect.

I like to rotate my spies once in a while. I figure if I’ve got a spy on an opponents planet, they will then have to divert funds to create their own spy to nullify him. Unless you’re the only other person in the galaxy, once that nullifying spy is made, if you’ve moved before he uses it, he’ll place it on some other person.
Some people like to save up 3 spies, and then place them all at once on an opponent. This can really cripple his production or research depending on what you use them on. This will also insure they can’t immediately nullify your agent.
Each spy costs more than the last one. So don’t waste them. If an opponent easily nullifies your spy, don’t just stick one more spy on their planet. It could be a losing money sink.
Spies cost nothing to maintain…
If you’re bringing in lots of extra money and don’t know what to spend it on, you can crank your espionage slider to use up to 25% of your production cost towards making spies.
To nullify an agent click the Domestic Stats button, and then the Espionage tab. If you have an unused spy, you’ll be able to highlight the enemy spy and click nullify.