Rings can be obtained by creating different boxes containing said rings. You can create these boxes at a Ringcrafting Bench
Rings cannot be upgraded or have their stats added/increased by using tentacles of Q'bthulhu or pearls of wisdom. There is also no way to modify the drop rate of higher tier rings, including magic find and location when opening boxes. Currently the best observed rates put shadow 4 drop rate at approximately a 0.25% chance.
On Live, the highest rarity is shadow level 4.
On the Public Test Server, Rings have Shadow Level 5, Radiant (levels 1-5), and Stellar (levels 1-5) rings. These new rings can be crafted in the Lord of the Rings section of the Ringcrafting bench (With shadow, radiant, and stellar having its own box).
You also will get 75 Mastery Points when reaching a new ringcrafting tier.