how to plant spies

There's a little Spy icon on the left side of the Hud just above the Research box. Click that, then click a planet.

Alternateively, on the 'Finance Management' window, 'Espionage' tab, there's a 'Place' button below the spending % slider. Click that, then click a planet.

You can click the planet in question and on the right hand side of the HUD next to the 'speak to' button should be a 'place spy' button.