This quest begins immediately after you have confronted Nikolaos. Regardless of your decision, you will have to leave Megaris at this point to continue the main storyline.
Note: If you chose to kill Nicolaos, you will have a large bounty on your head which will increase for as long as you are in Megaris. You should get out of the region as soon as possible.
Summon your horse and make your way to Barnabas. He will be waiting on your ship in the bay of Megaris. Speak with him and go through the dialogue options. If you choose to consider seeing the Oracle of Delphi you will have two objectives, but first you should go to Phokis to collect your reward from Elpenor. When you are done speaking with Barbaras, the quest will complete.
Did you Know?: The Oracle of Delphi is a contentious figure in the study of ancient Greek civilisation. It is still widely debated whether those who worked closely with her actually believed in her sacred powers, or whether they knew that she could be used as a political tool to influence state and regional affairs as and when paid for by powerful elites. One thing is for sure; the power perceived in her role allowed for it to persist for nearly five centuries.