Copernics are a new type of ore that was added to Warframe in the Rising Tide update. This ore can only be mined on Orb Vallis, and only drops while farming red veins of ore. You can find red veins just outside the entrance to Fortuna, and a good place to mine is in the cave system near the Central Maintenance.
To farm ore on Orb Vallis, you will need a Nosam Cutter from Old Man Sumbaat in Cetus or a Sunpoint Plasma Drill from Smokefinger in Fortuna. Both of them can be purchased with Standing for the relevant Syndicates. To earn Standing, do missions for Konzu in Cetus, or Eudico in Fortuna.
Equip your mining tool to your Gear wheel, and then load into Orb Vallis. When you choose the mining tool from the Gear Wheel and hold it in your hand, it will populate markers for ore veins on your minimap, as long as they are within a certain radius. It will also emit a beeping noise that grows in frequency as you get closer to a vein. Veins appear as blue or red lines on rocks, but to get Copernics, we are interested in the red veins.
When you find a red vein, aim at it with the mining tool, and one to three brights spots will appear on it. Hold down the trigger button to fire at one of the spots, then carefully watch the colored bar the will build up around the center of the screen. There will be a target that you need to hit, denoted by some white brackets. These can travel back and forth, remain still, or be very thin. Ideally, you want to stop firing when the colored bar hits the center of these spots. The more accurate you are with this process, the more resources you will get from mining the vein.
Copernic drops are random; there is no way to know if a vein contains Copernics until you mine it, so travel from vein to vein, mining the red ones to get Copernics. The amount of Copernics you get will be affected by Resource Boosters and the Smeeta Kavat’s Charm ability.
Once you have your Railjack built, the easiest place to farm Copernics is actually Railjack missions. You can get hundreds of Copernics from completing these missions. They drop from dead enemies, glowing asteroids, containers, and red glowing mines that can be found in all the levels. If you need to farm this resource, just don’t extract when you finish a mission. Instead, travel through the level, breaking asteroids and containers with your weapons, and collecting the loot that they drop.