You will be given this quest at level 20. It will appear in your quest log so there is no having to go somewhere to find it and accept it. The first thing you will need to do is speak with Heimdall at the entrance to Pandaemonium.

Heimdall Aion Level 20 Stigma Quest

You will want to turn in your quest to him and accept the followup. Now you will want to return to the Newbie Starter Island of Ishalgen and fly to Autroon Crossing. To get to the starter island again speak with the Teleporter NPC. Once you arrive at the newbie island head northeast again and speak with Munin. Below is a map just incase you forgot where he was:

Heimdall Aion Level 20 Stigma Quest

After you turn in your quest to Munin you will want to return to Auntroon Crossing and fly to Aldelle Village. Here you will want speak with Urd, whom gave you a card earlier in your life. After you speak with Urd you will want to speak with Verdandi in Munihele Forest, kinda remembering the pattern now?

After you speak with Verdandi in Munihele Forest you will want to speak with the final NPC, Skuld. As with before Skuld can be found close to the Coast just south of Autroon Crossing. Skuld will port you to a new area, called the Space of Destiny. When you speak to her here she will show you a quick cutscene.

She will then have you equip your Stigma Stone. To do this open your inventory and drag and drop your Stigma into a Stigma Slot.

Heimdall Aion Level 20 Stigma Quest

After you’ve done that you will want to speak with Skuld again. After you speak with Skuld Hellion will come out at you, remember this guy? Well now you get the chance to kill him! Kill Hellion and then speak with Skuld again. Skuld will port you back to Munin whom you will need to speak with again.

After you speak with Munin you will have the final part of the quest. You will need to return to Pandaemonium and head to the Capital Building to speak with Aud. Below is a map of where you can find the capital building.

Heimdall Aion Level 20 Stigma Quest

After you speak with Aud you will gain the ability to equip Stigmas. Speak with her again and select the “Equip/Remove Stigma” Option and equip your Stigma.