Your relic boost depends on the position of the map where your city spawned. You can identify your boosted relics by going to the world map and hovering over the grey round button on the bottom center right with the exclamation point. (This works on browser, I don't know what works on mobile.)
Your boosted relics can also be determined by looking at your research tree. The first "boost" will be indicated after the research for the marble, steel and plank factories, the second in chapter 2 after you research silk, crystal and scrolls, and the third in chapter 3 when you research elixir, dust and gems. You don't have to have done the research to scroll over the tree and see them.
You gain relics by completing encounters in map provinces. You can also obtain relics by completing tournament encounters, by crafting them in the Magic Academy, or in neighborly help chests.