On your travels throughout Skyrim, you might hear a rumor that the Bards college is looking for recruits, and to speak to Viarmo if you are interested in becoming a member of the Bards College. You will hear similar things if you talk to wandering bards or bards singing in inns and taverns.

The Bards college can be found in Solitude. If you been there, just fast travel. Otherwise, hire the horse carriage from outside whiterun. In Solitude, go Southeast from the town center to arrive at the Bards College. Enter the college and find the headmaster, Viarmo. Tell him you would like to apply for the college. He will say he has a task for you if you want to join. Elisif has forbidden to perform the Burning of King Olaf Festival this year and he wants to change her mind by reading King Olaf's Verse to her. Unfortunately that verse was lost long time ago. But according to his historian Giraud, the portion of the Poetic Edda dealing with King Olaf's verse might still exist in Dead Men's Respite. He needs you to retrieve the poem.

Tending the Flames
I have applied  at the Bards College. As part of the Application, Headmaster Viarno wants me to find and bring to him King Olaf's Verse.

Find King Olaf's Verse

The fastest way to reach Dead Men's Respite is to hire a carriage to Morthal, and from there head west, taking the bridge across the river.

Enter the Respite, and descend the stairs. In the next room, you will see a ghost! Approach it, but it will fade through the door. Take the Ruby Dragon Claw from the desk. This will raise a pressure plate and cause some Draugr to rise from their tombs and attack you. Kill them, then follow the ghost through the gate. Watch out for traps along the way. Activate chains to open doors. After reaching a junction, head west to find a small chamber with cobwebs. Destroy the cobwebs to reveal a chest you can loot. Head back to the corridor and go south, pull the chain to reveal a corridor to the east, filled with more Draugr skeletons. Work your way through them, turn North at the middle junction, then turn west and find some stairs going down.

Descend the stairs. Enter a room filled with cobwebs and frostbite spiders, and kill them all. Activate a chain on the east wall. This will open the grate on the floor. Drop down to the water below. Work your way through the flooded tunnels. Reach a room with a Skeever rat and some more draugrs. Neutralize them and climb up  a wooden spiral ramp. Open the gate, which will activate a pendulum trap on the bridge in front of you. Carefully advance one or two pendulums at a time. Or if you are at full health you can just try and make a run for it.

Activate the chain after crossing the bridge, then go up another circular ramp. You will reach a big iron door. Open it. Go down the stairs and to a corridor. You can use the Arcane enchanter there along the way. For enchanting, you can choose an item to destroy and learn its enchantment, or combine an item, enchantment, and soul gem to create magic items. To Enchant an item, you must know an enchantment and have a filled soul gem to power the enchantment. Enchantments are learned by disenchanting (Destroying) enchanted items.

Go west and you will reach a sealed door, protected by a magical barrier. Turn back and go north. Defeat the Restless Draugr you encounter. You will find a door with an expert lock, picklock it if you can (optional) and the master lock chest behind it. Reach another chamber with a grate on the floor. You will be attacked by some more skeletons. Activate the chain on the south wall which will open the grate, then go down the stairs. Activate the handle to the left of the door.. You will open a small chamber, and the bard ghost you saw earlier is inside!

You cannot talk or interact with the ghost of Svaknir. But he had led you to his final resting place. On the  ground,  his skeleton is grasping the Verse book you are after. Pick it up. The ghost will disappear. Your objective now is to return to the Bards college.

Climb back up the stairs, going back the way you came. When you arrive near the sealed door from earlier, the ghost of Svaknir is there! He casts a spell at it and dispels the barrier, then sheaths his sword and charges in. Follow him.

You will arrive at the RUBY CLAW RING PUZZLE. There are three rings, with three symbols on each ring: Inner Ring, Middle Ring, and Outer Ring, with a symbol of a Wolf, Dragon and Hawk (or bird) on it. The solution to the puzzle is on the Ruby Dragon Claw itself! Look at it in your inventory. The order of the symbols is as follows:

Dead Mens Respite Puzzle

Set the rings to the correct position and activate the keyhole. If you solved correctly, the door will open. otherwise, you will set a trap.

Go in, then turn south to go up through some stairs. Enter a big room with some blue mist. This looks like a throne room. Svaknir will be there. He challenges King Olaf to a battle. The Draugr skeletons will rise from their seats one by one. Help Svaknir defeat them. Finally, King Olaf rises from his tomb.

After defeating King Olaf, approach the blue glyphs on the wall behind his tomb to learn the Word of Power: Whirlwind, Whirlwind Sprint. Search Olaf's Corpse to find King Olaf's Treasury key. Use the key to unlock the door to the East. Loot the chest, and activate the lever. Go though the tunnel and past another door, then continue south to reach the skyrim exit. Fast Travel to Solitude and return to the Bards College.

Tell Viarmo you found King Olaf's Verse. He will be upset that the copy is incomplete, and aged to the part that some of it is unreadable. It means he cannot read it to the court and convince Elisif of the importance of the Burning of King Olaf's Festival. Ask him if you can't just make up missing parts of the Verse. He says he supposes you can do that, but he has no idea what happened in between these verses. Your objective now is to help Viarmo reconstruct Olaf's Verse.

He will start reading the first verse. Persuade him that Olaf was a Numinex, a Dragon in human form. He will read the 2nd verse. Persuade him that Olaf sacked it in dragon form. He will say its highly unlikely so he can't write that in. Tell him Olaf ordered disguised troops to attack Solitude. He will love that idea. He will ask you to come with him to the court to present it. Your new objective is to meet Viarmo at the Blue Palace.

Exit the college. Follow Viarmo to the court. When in the palace, talk to Viarmo and ask him if we are ready. Then watch Viarmo perform Olaf's verse in front of Jarl Elisif the Fair. He will convinve her to hold the Festival. Viarmo will be very pleased and tell you that you have done a great service to them. Ask him if it means that you are a Bard now. He will tell you that you are to be inducted into the Bards College at the Burning of King Olaf Festival. He sends you to speak to Jorn who is in charge of preparing the Effigy and deliver him the good news.

Go back to the Bards College and speak to Jorn. Inform him the Festival is back on, He will tell you that they will start the festival at dusk, and to come back and talk to him after dusk, which means after 10:00 PM. To pass the time, you can go get a room at the Winking Skeever inn and Sleep until 10:00PM. Then go back to Jorn at the right time. Attend the Burning of King Olaf festival outside the college. There will be music and free food. Talk to Viarmo and he will induct you into the bards college. Watch the ceremony of the Burning King. He gives you a gold reward.

This completes the Bards College quest "Tending the Flames"