In order to start this quest, the player must have made it through the base game quest "The Way of the Voice". If the player has not made it this far, Sledrig will give the player Miscellaneous objectives that if completed will progress the base game's main quest far enough to reach that necessary point.
After completing "The Way of the Voice", Helvana will approach the player and direct them to speak to Sledrig.
All other features and questlines for Bards College are intentionally available before this point so that players who opt to do a playthrough NOT as the Dragonborn for a character can still enjoy the other features and storylines with that character. The remainder of the main quest of Bards College Expansion involves shouting and the player being Dragonborn.
When the player approaches Sledrig, he will be finishing a conversation with Tyriana. After she leaves, the player can speak to Sledrig and he will reveal he "felt" the player was Dragonborn and that what he really wanted to teach them was to improve their Thu'um.
He will then ask the player to inspect the mural in his study.
When the player interacts with the mural, they will be brought to Sanctuary - a desert-like pocket dimension that Sledrig uses to practice and study.
Here, the player will be invited to learn about Resonating Shouts. Sledrig will first demonstrate it himself.
Sledrig will then place a Resonance Crystal in a stand just to the left of center and ask the player to use a Shout they wish to capture. The player can then use any Shout, and when they do the crystal will shatter and an Echo will appear (a humanoid for most shouts, though a few dragon-related Shouts will spawn a dragon Echo instead).
Mod added Shouts won't natively support the Resonant Crystal enhancement system and so would need a patch to be used to satisfy this part of the quest.
Mod Authors: A tutorial can be found here for adding support for 3rd party Shouts to the Resonance Crystal system!
Sledrig will then instruct the player to defeat the Echo. After they do so, a Resonance Crystal will appear on the corpse for them to loot.
Once the player has the Crystal, they will be asked to demonstrate it (by using the Shout again).
After they do so, Sledrig will hand them three more Resonance Crystals and give them an optional objective to explore the Sanctuary. He will also give them an optional objective to locate a tablet that will help them return there more quickly (see Sanctum's Resonance Shout for more details). Finally, he will tell the player that he will send for them when he is ready to teach them more lessons.
Objective markers will now appear on various objects throughout the area. If the player approaches any of them, Sledrig will comment on their purpose.
Once the player leaves, by activating the portal near where they entered, they will be returned to Sledrig's study where Helvana will be waiting.
Helvana will inform the player that she saw them go in, and imply that she knows a lot more about all of this than the player might expect. She will recommend the player go learn more from the other teachers. The quest will complete after the conversation with her.
72 hours after this, a Courier will approach the player the next time they are near a settlement and deliver the note "Letter from Sledrig", which will start the next quest.