UPDATE - Sony has updated the path to gaining faction since this guide was constructed. Currently it appears that each mission can be obtained at any faction and is repeatable, making it far easier. In addition tasks which previously only raise Wraithguard now can raise Leadership as well, such as Runic Ivory. I'm leaving the guide as is, but use whatever path you desire to hit ally, then jump to the Fergarin steps.
The first goal of Frostcrypt progression is to obtain Ally faction with Wraithguard Leadership. Everybody defaults to Dubious to start with them. As your faction improves, more tasks are available to you to continue towards ally. Which tasks are, and which are not repeatable is currently in flux.
Dubious - At starting faction there are only 3 ways to go up. First is to kill named mobs in the uninstanced version of Frostcrypt. The second is to tag boss mobs on an existing Frostcrypt raid (large hit). The third is the task Shade's Bane.
Apprehensive - The only new task at this level is Warning Signs
Indifferent - Once indifferent three more tasks open up, Wraithguard Vengence, Lodigar the Recruiter, and Incursion.
Amiable - A few tasks open during amiable, though perhaps not all at once. First is Orcish Dissention. You also gain access to the two main repeated tasks, Shade Bounty and Weapons Acquisition.
Repeating tasks as necessary, you can obtain Ally faction to the Leadership. Once ally, speak with Heimgul. He guards the tunnel that leads to Fergarin (your goal). However, to let you passed he requies a bribe of 3 "Mark of Rallos Zek"s. This may also require ally to non-leadership, but unsure. If so you can gain that faction killing in Frostcrypt, as well as doing various tasks in Valdeholm.
In the back area you find Fergarin Bardon I. He has 3 group tasks that must be completed to open up raids. They are offered in order, however you get credit regardless of order:
You will receive a flag once all 3 are finished, and you are now ready for raids.
The first raid Fergarin offers is for Kill Kangur, the giant spider queen. Upon completition of the raid, everybody receives a "Letters of Evidence", save them. The second raid is for Udengar the Traitor, where you use the Letters. If you run out of letters, and need to repeat Udengar, you'll need to redo Kangur to restock. Once Udengar is taken care of, you are offered the last Valdeholm mission, Speak with the King.
With everything up to this point completed, the first Frostcrypt raid opens. Defeating Hearol and Grenwald in FC1 opens up the second Frostcrypt raid, where you find the Shade King.