Gathering in Riders of Icarus is easy. You'll stumble across ores and plants all throughout the world.
Follow these three steps to success:
1) Walk up to all interact-able items that can be gathered along the ground.
2) Press the 'F' key or Right-Click with your cursor
3) Press the 'F' Key again to collect raw materials
Some plants and ores give you special items that are required to tame familiars.
Starting Area - Brakarr Forest
You'll be introduced to gathering by accepting a quest early on. You'll need to collect 3 Poron Mushrooms, which just so happen to be abundant all over the region. You will also find Copper Ore and Silver Ore in this area.
Hakanas Highlands
You'll find Gold Ore, Iron Ore, Poron Mushrooms, and Sage Grass in this area. Sage Grass has a chance to drop a secondary material, called Giant Nettle, that is required to create a potion to tame an elite familiar named Hoonbaba. And a third item, called Glowing Sageweed, that is required to tame Logash or Rogaton the White. Hunter's Cave (Solo Story Instance mode) is a great place to farm Gold, Iron, and Sage as it respawns quickly, even after all quests and Jack the Hunter is defeated.
Parna's Coast
You'll find Amethyst Ore, Mithril Ore, and Cherpa Snow Flowers in this area. Cherpa Snow Flower has a chance to drop a secondary material called Shining Cherpa Snow Flower, which is used in crafting taming items. Amethyst Ore has a chance to drop a secondary material called Shining Amethyst Ore, which is used for crafting an item to tame Blue-shelled Turtles.