On your world map, each province you scout yields a particular goods relic. You will see the good as an image. As you scout these provinces, they become eligible provinces for tournaments of that particular good, when a tournament is going on. So, a marble tournament will open up in the exact spot on your world map where you scouted a marble province. The first one is the one closest to your city. Then, as you complete the tournaments in those provinces, more will become available in other marble provinces that you may have scouted further from your city. In each tournament there are multiple rounds that you can play every (I believe) 16 hours, so keep replaying the same tournament in the same province for more rewards and a higher score.
Also, someone can fact check this for me, as it's only a vague memory, but I think you have to unlock a certain amount of tech on the tech tree before you can participate in tournaments? Again, not sure on that one.
Hope that helps.