Nope you don't have to build something on a trade resource to get it's effect.  As a matter of fact, you can't build anything on them at all (you can destroy them to make room for buildings if you want though).  They work by giving you whatever effect they say they have; all you have to do to receive their effect is to own the planet they are on.  And their effects are cumulative, despite what the misleading descriptions say.  So if you have 3 different planets with a trade resource that give +5% to shields, that means all of your ships will have their shield value increased by 15%.  You can also use trade resources in the diplomacy screen, to trade for techs or cash or whatever you can get for them.

 

Hope that helps.