To earn those Renown ranks, players be given two weekly quests in WOTLK Gold combination with the Covenant's story quest. Each of these quests will award an Renown rank-up.
The first of these will almost always task players with the deposit of 1000 Anima into the reservoir of the Covenant at the Sanctum. Any Anima that the player has prior to the quest being live at the beginning of each week's week won't count towards the required amount.
The players must instead farm Anima by either using the Covenant's zones or by fulfilling other quests, picking up, or even hunting rare spawns.
The second quest of the week will task players with rescuing Lost Souls. To accomplish this, they'll be required to go into The Maw and recover souls from the tower Torghast.
Every week, they will get a different soul for the realm of their Covenant to help. These Tormented Souls can eventually turn into Redeemed Souls which can be used to buy WOTLK Gold enhance the Sanctum.