The Baldur's Gate 3 Wyrmway dungeon is a little like a late-game Gauntlet of Shar; a series of trials you've got to complete if you want to reach the Dragon's Sanctum. Completing this is a key part of Wyll's quest if you rescue his father from the Iron Throne, and has some knock-on effects on Karlach's quest, too.
Completing the Wyrmway also rewards you with two Legendary items, and a key bit of lore that might help inform which ending you choose. If you've got the time in act three, it's well worth pursuing. Here, I'll walk you through each of the Wyrmway's chamber trials and how to complete them so you can face Ansur, as well as how to enter the Wyrmway.
How to enter the Wyrmway
As the name implies, you can get into the Wyrmway via Wyrm's Rock fortress. Head down into the prison via the staircase in the room with the Wyrm's Rock waypoint. Pass through the door by the guard, then turn left and go to the end of the corridor. You'll find two Dragon Head torches. Turn these off and then deal lightning damage to each of them—through a spell or an Arrow of Lightning—then turn the torches back on. Both will glow white and reveal a door into the Wyrmway.
Chamber of Justice
From where the dragon door is located with the four statues of Balduran flanking it, head left down the stairs into the open area filled with paintings. This Chamber of Justice is all about determining the guilt of the character depicted in the paintings around the room, and granting him a fair punishment based on his crimes. To do this, you need to use the Remove Curse spell on the judge in the centre of the room to reveal the three paintings near him. Each painting depicts a punishment you can choose.
While the character in the painting didn't commit the crime he was accused of, he did commit a different one, so you should opt for "The Cell" painting. Pick it up and activate the Empty Niche opposite the paintings to place it and render your judgement. Statue Balduran will be very pleased with your fair-handed treatment.
Chamber of Insight
The next statue in the main room takes you across a magical bridge to the Chamber of Insight. This puzzle involves everyone's favourite pastime: reading. Oh, and also catching flying books. You'll have to stop the books in order to read them, using the information to determine which of the three figures standing on the raised altar is a threat to the city's peace. I use the Command spell to make the books halt, but if you don't really want to do the puzzle, I can just tell you that the answer is Suelto. Attack their ghost to finish this trial.
Chamber of Strategy
I hope you like chess puzzles, because that's what you're going to be doing in the Chamber of Strategy. Also, the bad news is that the chess problem is different for everyone, so if you want to do it properly, you're going to have to find a way to defeat the Black King in two moves yourself. The good news, however, is that you can actually just use a lightning spell to kill the Black King and win the game outright, since lightning damage against it is doubled. You'll have to kill it in a single spell, otherwise it'll heal, but I just brought out Gale and used Chain Lightning, though Lightning Bolt will also get the job done.
Chamber of Courage
No puzzle here; just plain old survival. Once you pick up the torch, you'll need to stay alive for four turns as elementals and myrmidons spawn around you. I'd suggest casting Abjuration spells on whoever has the torch, and then focusing down the enemies as they spawn so you don't get overwhelmed before the end.
Now that you've completed all four chamber trials, you're ready to head through the dragon crest door to face Ansur. I'd suggest resting first as you have a tough fight ahead. Ansur has 400 HP, which is the same as a Red Dragon, plus he has an annoying lightning AoE that's tricky to avoid unless you get behind cover.
Still, you can chip his health if you surround him, bring minions, and keep closing him down into melee. Though you sadly won't recruit the dragon to help you in the final battle, you will get two Legendary items for all this trouble. The Balduran's Giantslayer greatsword, which you can loot from Ansur, and Balduran's Helm, which rests on a podium at the back of the room.