Speak to Anastase and select the invisible chat option to begin the quest.
Select a difficulty level to receive an assigned zone.
Your target fount depends on the difficulty setting you choose (see the sections below).
After selecting a difficulty, you are warped to a random zone corresponding with your difficulty setting. You appear some distance away from the zone's Geomagnetic Fount. You must return to that area's Geomagnetic Fount and examine it.
Accepting this quest will temporarily reroute the relevant Waypoint until the quest is completed. For example: if the quest took you to Jugner Forest (J-11), then teleporting there via Waypoint will take you to (J-11), rather than the usual (G-5), until you complete the quest.
Speaking to Anastase will end the quest, regardless of whether you checked the Geomagnetic Fount in your destination zone, but you must have checked the fount to receive full rewards from the quest.
Currently, it seems that the only purpose of this quest is to obtain Trail Cookies, EXP, and Conquest Points. Even though the quest dialogue mentions the founts deteriorating, it does not appear that you can ever lose access to them completely.
Some fount data has destabilized, causing travelers to be warped to unexpected locations. Use the waypoint to travel to these locations and re-record the data. Beware -- you may not end up where you wanted to be.