Tellurium is an incredibly rare resource in Warframe, with a meager drop rate. You will need this to build parts of Warframes, weapons, Archwings, and other in-game items. Unfortunately, Tellurium only spawns in Archwing missions, the Grineer Sealab tileset, and Griner Asteroid Fortress missions.
The best node to farm Tellurium on is Ophelia, on Uranus. It is a Survival mission, so you can run it endlessly and enjoy the benefits of increased drop rates as the mission goes on.
You can use Resource Boosters to increase the drop chance of resources, and the amount you get with each drop. You can purchase them from the Market place for Platinum. If you are a member of a Clan, it is worth asking veteran players to run a mission with you and bring some farming Warframes like Nekros, Hyrdoid, or Khora to increase your chances of getting some. You can also increase your drop rates by bringing a Smeeta Kavat, thanks to their charm ability.
If you are not a member of a Clan, then head to the Recruiting Chat and find people looking to run a Tellurium farm and team up with them. With Tellurium being such a rare drop, it truly helps to run with a squad.
When running with a squad, it is a good idea to run two farming frames, a Trinity to keep them stocked with energy, and a stealth frame like Ash, Ivara, or Loki. With your squad, find a section of the map with a room that only has one entrance, and camp there. Kill enemies with abilities that farm the drops, have Nekros use Desecrate, and send the stealth Frame out occasionally to top up life support. This strategy will maximize your resource drops, and you will end up farming more Tellurium than you can via any other means.
If you get desperate for Tellurium, you can purchase it from the Market for 10 Platinum, although this method is not ideal for resource farming.