Talk to Yuleph Phan, in Kalikori Village, on Tython. This is a level 4 quest.

Yuleph Phan: More young Jedi in Kalikori, I see. I am Yuleph Phan, master of rituals. I welcome you. You wish to participate in the ceremony I presume? You understand the dangers?

Ask him about the Ceremony. He tells you that many of your brethren, your "Padawans", come to Kalikori to perform their rite of passage. Those who endure the ceremony are awarded an audience with Kolovish to receive her wisdom and her gifts. You can say:
Please explain
Padawans do this?
I doubt it'd be challenging.

Choose the second option, to ask him why Jedi would participate in Pilgrim rituals. Yuleph tells you they do that to prove their strengths, gain rewards, and show friendships. Kolovish lives in the mountains above. Once their leader, now she is their guide and protector. To complete the ceremony, you must walk the thousand steps to her home. You must carry a burning brand and light the signals along the path. You must protect the flame from beasts and Flesh Raiders. This will prove your worth. If you wish, Yuleph will ignite the brand. It burns only a short while, but if you are deserving, it will be enough.

You can choose to either light the brand (accept the quest) or  tell him that not today (refuse the quest). Tell him you are ready to carry the flame. He tells you to go and light each of the signal fires along the mountain path. When you reach the end, you will find Kolovish.

You receive the Burning Brand from Yuleph. Open your mission log:

The Thousand Steps
Yuleph Phan, master of rituals in Kalikori Village, has offered you the chance to complete a dangerous rite of passage that will prove your worth o the villagers. To complete the rite, you must light the signals along the path to Kolovish, a revered former Matriarch who now lives in the mountain of Tython. Many Padawans have attempted the rite, but not all have succeeded. Take the burning brand and light the signals along the path to Kolovish's home.

SWTOR The Thousand Steps

Your task will now be to light the first signal. Take the road behind Yuleph, climb it into the Matriarch's Summit in mountains to the east. Ignite the first signal fire, then continue your trek up the road to light the second signal fire. Check your map occasionally to make sure you are on track. There are some enemies along the way, such as Flesh Raiders and Enslaved Cthons, but if you stick to the road you will be able to avoid them.  If you do want to kill them, you will get a bonus quest: Clear the Mountain Path which requires you to defeat the Flesh Raider Slavers and Slavemasters who are harassing Twi'leks on the mountain path.

There is also a boss in this area, Mar'gavrok, a level 5 Reaver with 1100 HP.

Once you have lit all three signals, you need to speak to Kolovish. Continue up the path (is anyone counting if there really are one thousand steps?), and reach the tower on the top of the summit. Climb the spiral ramp and talk to Kolovish.

Kolovish: You perform the rite of the Pilgrims well, Jedi. I saw the signal fires as you climbed the path. Very few of your kind make it this far. I am Kolovish, first Matriarch and reader of the ancient texts. I led our people to this planet, and I welcome you.

You can say:
You led them here?
Thank you
My prize, please?

Thank her and tell her it is a privilege to meet her. She says she is privileged to meet a Jedi who accept the Pilgrims' ways. Even their own kind, the other Twi'leks, they mocked them and denied the authority of the Matriarchs. This is why she led her tribe here. Now you have completed the ritual and you are friend to the Pilgrims. You share their burdens and you share their strength. Tell her you are honored. She gives you some gifts and tells you how as a Jedi, you share her world, and you face a difficult future. Ask her why she thinks your future is difficult.  She tells you that it is the way of Jedi to face darkness. She believes you will face the darkness of our world, and perhaps beyond.

This concludes the quest, The Thousand Steps.