Finding a way to Verdania in is kinda confusing. [[link]] It's definitely one of the most complex regions to reach, especially as I'm pretty sure it's entirely optional. First off, actually visiting it requires you to , which is a whole elaborate process in itself. You'll also have to complete some additional unrelated steps before that.
If you hadn't clocked it, this all involves the Green Prince—a mysterious grasshopper (he might be a cricket…) you can rescue in Sinner's Road. Visiting Verdania is related to his overall journey. Obviously, this guide will contain some spoilers for the Act 3 main quest (as far as having to progress it to reach Verdania is concerned), so leave now if you're not there yet. Otherwise, here's how to unlock Verdania as an area and help the Green Prince.
How to unlock Verdania in Silksong
As mentioned above, you can't get to Verdania until you're in Act 3, and even then, you'll have to jump through some hoops first. I suggest doing these first three stages during Act 2, because I can't 100% confirm you still can in Act 3.
Rescue the Green Prince from his cell in Sinner's Road
For this first step, you'll have to head to Sinner's Road via Greymoor. The entrance to this area is directly above the Halfway House—you'll want to climb the big building on the left of Greymoor with the Chapel of the Reaper at the top, and then head right along the upper walkway to unlock the lift back down to the Halfway House. Now, keep climbing and going right and you'll find Sinner's Road. Head right through the initial chamber into the main shaft, where you'll find the Green Prince just up and to your left (though you have to drop down to reach him).
If you don't have a (and have used the one you can buy from Pebb in Bone Bottom), there is another in Sinner's Road. Simply make your way up the shaft the Green Prince is in (you'll have to climb the hanging cage room to your right), then head right along the corridor at the top of the shaft, and up the next shaft where there's a Roachkeeper miniboss you can kill for a key.
Meet the Green Prince in The Choral Chambers
Once you're in Act 2, you can meet the Green Prince in the lower left side of the Choral Chambers, just to the left of the Citadel Spa and down the shaft from the entrance to . This is a brief encounter, but it's necessary to get him to move to the next location.
Beat the Cogwork Dancers and meet the Green Prince again
The Cogwork Dancers boss is located [[link]] at the top of the Choral Chambers and is necessary for you to progress the main quest. Once beaten, head back to the arena and hop up onto the left side entrance to find the Green Prince there examining one of the automatons. Speak to him, and you'll have done everything you can in Act 2 to progress towards Verdania.
Get to the next act and progress The Dark Below quest
This is where things get a bit more involved. You'll have to to open the way to the regular version of Verdania to the right of Craw Lake in Greymoor (the arena where you fought those annoying birds). This regular version of Verdania doesn't have much in it save for a mourning Green Prince.
To unlock Lost Verdania (the true version), you'll have to progress the main quest a bit. Head to Bone Bottom Chapel as directed, go to the Deep Docks and unlock the diving bell (by speaking to Forge Daughter and Ballow and then going through the Simple Key door to find the route), and then head down to The Abyss. Once done there, you'll come back up, visit Bone Bottom Chapel again, which is where you'll learn Elegy of the Deep on your Needolin.
Now you'll want to head back to the Green Prince and play that song onn the Needolin where he's standing. This will let you enter the Green Prince's memories, unlocking Lost Verdania (the full version of the area map), so you can explore and delve into the region's past.