From
http://oldforum.paradoxplaza.com/forum/showthread.php?563846-Prospecting
There are three ways to find hitherto unknown resources:
1. Finding new resources in national territory. For this, you'll just have to build a prospector unit and there's a chance per turn to find new resources. The prospector unit does not have to be adjacent to the province where you find new resources. In national territory, the "newly" found resources are actually the resources which were already known in earlier versions of the game, at least that's my impression from my Japan game. So if you've already played a previous iteration of the game, you should roughly know what you can expect to find.
2. Finding new resources in colonial territory: This also needs a prospection unit and you play the corresponding colonial card to find new resources. I guess you can also find new resources in colonial territory by the above mentioned way, as long as you have high enough military control or loyalty (not sure, but it should be something like this).
3. Scripted events for certain special resources: This largely affects gold, gems, oil and rubber. Those events will trigger automatically, just wait for them to occur. You don't need a prospection unit or anything else.