Tihyo

To obtain any of the tiered gems you have to kill mobs. All vanilla and modded mobs have the chance to drop a gem. Depending on the tier of the mob, they have a 10% chance to drop the mob's tier plus two tiers below, with a higher chance to drop a gem of its tier. For example, a Pigman Brute is a tier 5 mob so it has the chance to drop a tier 3, 4, or 5 gem, with it most likely dropping a red gem.