Vainthorn is the newest material added in the Abyss of Dagath update; it serves as the core resource in building Dagath, and is needed in abundance. Getting Vainthorn is pretty easy to obtain, but it is a bit of a grind if you're looking to make use of the stuff sooner rather than later.
How to get Vainthorn in Warframe
Vainthorn only comes from a location in Warframe called the Abyssal Zone, which is located on the planet Ceres. The Abyssal Zone functions like your standard Warframe mission node, but it requires you to have an Abyssal Beacon in order to be accessed. In fact, if you don't have an Abyssal Beacon, you cannot see the Abyssal Zone even if you scroll to it on Navigation.
Abyssal Beacons can be purchased from any of the Faction Syndicates, such as the Arbiters of Hexis, Steel Merdian, and New Loka.
Regardless of the Syndicate you're pledged to, you'll need to be at least Rank 2 in it to purchase the beacons.
Abyssal Zone is a special variant of the Exterminate gameplay mode in Warframe. Completion of this mission will reward you with six to eight Vainthorn per run(eight to twelve on the Steel Path). This mission can be played over as much as you desire so long as you have Abyssal Beacons to use for it.
For more helpful guides and useful information relating to Warframe, check out All Grendel Prime Relics in Warframe and How To Get Them right here on Pro Game Guides.