Im not exactly sure what they're called, but the silver coins that is the default money. But I can't seem to get these monies at all. Is there a secret that is only reserved for the coolest of users? Or am I just missing something obvious?

At this point? Just explore and do quests, that's really all there is to it.

Try every day to do the quests available to you. You will not always be able to do them all, but it will give you a decent amount every day.

And the biggest portion is simply explore, explore, explore. Explore not only gives you resources, you will find piles of silver lying around and even more in treasure chests that you get. Also you can get special items from chests, like blueprints for buildings or even potions or scrolls otherwise only available in the Premium Store. These you can then sell on the Trading Post for silver (just be advised that blueprints don't sell really well, but it doesn't cost anything to put sales up so just try again if it doesn't sell - items like Rainbow Jars, Mutagens or Scrolls of Insight on the other hand sell very well). 

Also, the higher level a pet is, the bigger the amount of silver is it will find in chests and piles. And every 10 levels, the islands a pet visits get bigger, meaning more resources, more chests and more piles of money. So get 10 - 15 pets, level them with exploring and eventually money will start rolling in.