Note: When talking to Curilla she will offer you the The General's Secret if you have not done it already. Accept this quest and talk to her again (you do not have to zone) to start your artifact quest.
Go to the basement of the Cathedral in Northern San d'Oria and speak with the priest, Pagisalis. He will tell you to fetch a piece of Velvet Cloth if you are to pray there. Fetch him the cloth and trade it to him.
-Note: Once accepting the initial cutscene with Curilla, this entire quest can be done as a job other than Red Mage if necessary. You can use a Thief to pick the Treasure Chest and you will still get the Crawler Blood.
Go back to Curilla for another cutscene.
Go back to Crawlers' Nest and bury the boots by clicking on the ??? at (I-10) on the bottom floor of the nest. Note that this is the northern basement (the one with the zone back to a plateau in Rolanberry Fields).
Leave the boots there until 12AM JST (11AM EST(10AM EDT)/3PM GMT), and then click again on the ??? to retrieve your boots.
Return to Curilla if you wish, as you will need to return to her to quest for your Chapeau anyway.