You get the "perform noble deeds" quests from Tyra again. Looks like going forward this will be a weekly repeatable quest to eventually get all the artifacts

Ah, ok. So it's the REALLY general one, not the 15 patrol beacons one.

(Unless you do the 3 character method to get 3 in one week instead of just 1.)

Heh, if by "3 character method" you mean "happen to play 3 characters anyway," then that's what I'm doing.

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If you are looking to do PvE, I'm your huckleberry.

I've actually been visible lately, too. Just saying.

I haven't figured out how you earn artifacts yet. I just got the one from the quest line. Can anyone share the details here?

As you know, the new Iron Lord Artifacts can be obtained by completing a weekly Shiro bounty. This awards an "Iron Lord Legacy" item that can be turned in to the Fellwinter Cryptarch in exchange for one of the week's 350 LL artifacts. If you complete the bounty on three characters, you can pick up all three artifacts available this week.

Obtaining Light-Levels Artifacts >365:
Artifacts are very common roadblocks to light level increases. There are many opportunities to get light level increases for armor, weapons and ghosts, but light-leveled artifacts are rare. Legendary engrams can not decode any higher than 365 LL, including any that turn into Artifacts. Artifacts aren't available from Vendors, Faction Rank-ups, Exotic Engrams, or Quest/Mission rewards either. Artifacts greater than 365 can only be obtained from Eris Faction Rank-Ups or from Strike Loot chests that require a skeleton key.

Eris Reputation:
Eris requires 3000 reputation to receive a faction rank-up package. Her packages have a chance of including a light-leveled Artifact. If you don't get an artifact, you'll get a light-leveled class item.

The best way to earn Eris reputation is to complete her weekly bounties. Each week, your first Court of Oryx completion will add a new bounty to your guardian that awards 250 Eris reputation when completed. When turned in, it will add a bounty that awards 500 reputation, and that in turn will award 750 reputation when complete. Completing all three bounties will award 1500 reputation, and they can be completed once a week for each character. The remaining Eris reputation you may need can come from completing events at the Court of Oryx. You can earn 500 reputation by completing 10 Reciprocal runes (25 each), 3 Stolen runes (50 each), and 1 Antiquated rune (100 each). You can also gain Eris reputation in the Crota's End raid (25 per chest and 50 per encounter).

Heroic Strike Chests:
After defeating a Strike boss in a strike playlist, a chest will appear that can only be opened using a "Skeleton Key". When opened, the chest awards one item of strike-specific loot, and either a light-leveled class item or light-leveled Artifact.

Each character receives one skeleton key when they complete the Sepiks Perfected strike for the first time in the story. Additional keys are rewarded randomly as Strike completion awards. The drop rate for keys is low - it seems similar to or less than the Taken King drop rate for strike-specific loot. It is believed that the chance for a Skeleton Key to drop increases with the difficulty of the strike (Nightfall having the highest rate) and with the presence of a Strike Streak booster.

When to use:
Hoard your keys and your Eris Reputation rank-up package - these are rare and should only be used when your Artifact light level is holding back your light progression (to maximize their usefulness).

For a brand-new guardian, I would recommend not using Skeleton Keys or Eris until they already had a 365 Artifact (obtained via a legendary engram decryption) and all their other gear was high enough so their light level was 373-374. A light-leveled artifact at that point would immediately raise light level by one, and allow legendaries and exotics to drop up to 380+. I wouldn't use keys or Eris again until all gear was high enough to reach a light level of 382-383.

Heh - this is awesome advice, but I have to tell you - I've gotten 2 skeleton keys, total, after running about 30-40 strikes... and I'm sort of stuck at light level 355. So all this talk of 375+ is pretty funny stuff. ;)

"We are actively investigating an issue where the Winter’s Run Nightfall Strike is not rewarding Skeleton Keys."

Source

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tl;dr

The system sucks and is a horrible step back.

As you know, the new Iron Lord Artifacts can be obtained by completing a weekly Shiro bounty.

I didn't even know this. I've completed a few bounties of his and didn't see anything happen when I turned them in.