You can pick threads of fate anytime after completing your first 60.
As for @
Azerox comment. I disagree entirely. My last 4 characters have been through TOF and i average about 2-3 hours faster then story, based on kill speed of characters.
What you do with TOF.
Accept the quest to pick a zone in Oribos. Go to that zone and pick up the quests for that zone's dungeon. Dont run it yet.
Hearth back to Oribos
Accept the quest to pick a zone again and go to that zone and do the quests for that zone's dungeon quest.
Repeat until you have all 4 zones dungeon quests in log.
Now pick one zone, start filling the bar. Do NOT do bonus objectives. Do side quests and world quests. Pet Battle quests are great if you cheese them with level 1 pets (the quest will scale to your level, while still giving you full xp).
Once you get the bar to 80%, queue for all dungeons random. If you get the dungeon for the zone you are in, great, finish it. If you get the wrong dungeon, you can leave or finish the dungeon, your call. You want to random queue it because you get bonus xp for the random. Finishing the dungeon of the zone will put you at or around 100% completion.
Doing Threads of Fate will get you at least 4 renown (typically 8 renown) by the time you hit 60 and allow you to immediately begin using the covenant abilities. It helps a lot because Bastion is a ton of wait and talk quests.