Submitted by pchester:
The easiest way I have found is to head down the climbable cliff near where you first entered the Caves. Climb down and head right toward the north east corner of the map. There are teleports all along the centre of these sections, so it is quite easy to hit one ... which is what you want to do.
Having hit a teleport, you should find yourself at the end of a corridor on the opposite (west) side of the map. Face back toward the centre, and follow the wall on your right. This will take you to a bright area with a couple of mine carts and another climbable wall.
Climb up and through a one-way wall into a corridor on the top level. Look left and across the corridor. Near the corner of the opposite wall is a small opening. Be careful of Burners! You arrive in a large cave with a sloping floor. The Labyrinth transition is in the corner to your left. Go up the slope and down again to avoid the Electros...
Submitted by Sword2012:
An alternative explanation for the hopelessly lost...
Starting at the normal entrance to the Caves, with the stash bag and the minecart on its side in front of you
Go forward and turn right at the first junction, hugging the right hand wall to skirt a swirling Fog anomaly. Keep hugging this wall until you reach a sheer drop
Either drop down, using impact-reducing protection, or climb down this wall carefully by staying very close to the sheer face
Walk along the path, staying near the centre of it, until you pass through a teleport and encounter a wall right in front of you
Turn around and follow the new path, hugging the right hand wall
You'll reach a bright area with a minecart at the corner in front of you, and another a few paces further on. Climb the wall in the corner by the first minecart. Yes - it CAN be done...
As soon as you reach the top you'll pass through a one-way wall. There'll be two fires - one directly in front of you, and one on the left. Head towards the leftmost one. As you do, in the wall beyond the fire, on the right, you'll see a round shaft, or opening
Go through the hole, but watch out for Burners!
At the end of the shaft you'll pass through another one-way wall. Do not continue upwards, but to your left, hugging the left hand wall, past the Electro (you may need to go upwards a little to skirt your way around this anomaly) towards the transition point to the Labyrinth...