Guide to Guild Daily Quests in ESO

To start the daily quests for the Fighters Guild in ESO, you will first need to be a member of the Fighters Guild. You can join them by simply visiting the Fighters Guild Hall in Glenumbra, Auridon or Stonefalls. See this guide for more information about the location.
The daily quests are obtained from the Fighters Guild Hall that is located in the main hub city for each alliance. These are Wayrest in Stormhaven, Elden Root in Grahtwood (behind the throne room of the Upper Level of the Elden Root tree), and Mournhold in Deshaan. When you are there, find and speak to the NPC called Cardea Gallus. She will give you a daily quest. 

Cardea Gallus in ESOThe daily quests will always send you to destroy three Dark Anchors in a particular zone, which can be any of the base game overland zones except for Cyrodiil. You can destroy the same dark anchor multiple times. 

Once you have completed the objective, return to Cardea Gallus to hand in the quest. She will give you a Fighters Guild Merits container, which usually contains some basic consumable items like potions or food, some Ornate traited equipment which can be sold to a vendor, and may also contain a style motif from the Draugr style, or the associated style material. 

A Dark Anchor in ESOYou will also receive 10 Fighters Guild XP which increases your progress towards leveling up the Fighters Guild skill line. However this is a pretty small amount so if you're just aiming to level up the Fighters Guild skill line quickly, this is not a very good way to do it. In that case you would be best off just repeatedly destroying dolmens or grinding undead or daedra kills in a location where that enemy type is plentiful (Skyreach Catacombs is very good for this, but you may need a friend to help you depending on your build and your skill level).
Location of Fighters Guild in WayrestLocation of Fighters Guild in MournholdLocation of door to Elden Root Upper Level