This ring is rewarded by completing the last step in the chain that begins with the Grime-Encrusted Ring, a dungeon drop item within the Gnomeregan instance. To complete the quest, place the Grime-Encrusted Ring into the The Sparklematic 5200 found inside The Clean Zone in the dungeon. I found that only one of the three Sparklematic machines allowed me to insert the ring, so if the first one doesn't work, try the others.
You will also receive the quest Return of the Ring to return the ring to an NPC in Ironforge or Orgimmar, depending on your faction. Bring the NPC some additional materials and he will upgrade the ring to Nogg's Gold Ring.