Skyrim Walkthrough: A Return to your Roots

The best time to start the "A Return to Your Roots" quest is while doing the quest "Discerning the Transmundane" which sends you to Blackreach in search of the Elder Scroll.

While in Blackreach, locate and harvest a plant called a "Crimson Nirnroot" to start the quest.

Check your quest log once you have harvested the Crimson Nirnroot:

A Return to your Roots
I've discovered an unusual ingredient called Crimson Nirnroot

Your objective is to discover the significance of Crimson Nirnroots. Do not harvest any additional Nimroots for now - As you will need to harvest them later as part as a quest objective.

You need to locate Sinderion's Field Laboratory. The best way to find it is to go to the Alftand Cathedral Entrance. Enter Blackreach from there, and you will see a big stone building, which is the Sidnerion Field Laboratory. Enter it through the door which should be unlocked. Inside the building, on the ground, there is the Skeleton of Sinderion. Loot it for Sinderion's Field Journal.

Read Sinderion's Journal. This will complete the objective "Discover the Significance of Crimson Nirnroot" and start "Collect Crimson Nirnroot in Blackreach".

The journal reads:
4E58 Second Seed, Middas
I've spent a large potion of my life unraveling the mystery of the nirnroot and yet I still feel unfulfilled. The trilling sound this strange herb emits seems to taunt me, to push me even harder to discover its secrets...

Not it will be up to you to discover the secrets of the Crimson Nirnroot. You need 30 of them which could take some time. There is one in the Laboratory itself, make sure to get it. The rest are scattered around Blackreach. Run around the dungeon and collect enough of them. If you cannot find enough Nirnroots, you could go do some other quests, and return after approximately 30 days have passed and the Crimson Nirnroots should have grown back in many of the locations. The Nirnroots emit some light around them, and produce a subtle humming noise, which should help you spot them.

Once you have collected 30 of them, your task is to bring the Nirnroots to Avrusa Sarethi. The Sarethi Farm is East of Ivarstead. Speak to Avrusa Sarethi.Tell her you brought the Crimson Nirnroot for her. She tells you she will search through Sinderion's notes and find some more information about the Crimson Nirnroot and its properties. She gives you  a tome. It's one of Sinderion's greatest works.

Avrusa Sarethi gives you a book called "The Nirnhoot Missive". You also get a perk called "Sinderion's Serenpidity". This is an active effect that provides a 25% chance of creating a duplicate potion when using your alchemy skill. So whenever you craft a potion from now on, you have the change to get two potions instead of one.

This completes the quest "A Return to your Roots".