¶ Overview
The skew is one of the most useful techniques in the entire game. It basically allows you to snap in any room to a border as long as there is a counterpart room. Phasing through walls in the process.
¶ Explanation
The reason why this is possible is because you offset the active room from your current position. Your current position room is called destination room and the initial room where your screen locks onto is called source room. The picture below shows how it looks if you do so. You can see that the screen is showing the source room and the minimap shows where Indra is. 
If the source and destination room align. That means they share a skew border. Then you can invoke the transition because the game checks only along one axis if the destination room is aligned with the source room, but it doesn't check perpendicular to the transition. If you move with the transition from the source room to the destination room you can invoke the transition. This will drag you to the closest valid point along the transition axis.
¶ Example
For Example you are going one room up. So the game is only checking if the height of the active room aligns with the destination room. The game checks that you are only 1 room above but it doesn't care if you are maybe 20 rooms to the left or right. So the game executes a transition upwards and after you transition upwards you land always on the bottom of the new room and the game is just putting you were the bottommost valid position in that room is. You can see a situation here. Where S is the source room, D is the destination room and the line is the skew border: 
¶ Summary
To summarize you need to offset your position from the active room and therefore creating source and destination room. If you aligned them properly they do share a border together. You will skew along this border. Once you travel further away from that border in the destination room the game realizes that it needs to scroll and therefore doing a skew.
The skew is something that basically happens all the time as soon as you offset your room. But the crucial thing is to understand when it happens and how to prevent it. Almost any other technique builds on top of this one so check out them as well.
¶ Execution
How to execute it:
- Offset yourself from the active room (here we do drone warp)
- Move away from the skew border
- Skew is done
¶ Notes
A few notes:
- You can skew in any direction
- You can skew with Indra and the Drone
- If you execute a skew the destination room will turn into an active room
- You can skew as far as you want but only 1 room alongside the skew border
- You will always end up alongside the skew border
- If you savequit or teleport it does reset you source and destination room.
- If you savequit with the Drone Indra's rooms are still the same way
- This works in the breach as well
- There is a chance that you end up in an entirely new room, if you do so please report.
¶ Proof
¶ Setups
So this can be done in any room you can get in with a character while a source room aligned with the destination room is loaded. For the most important ones check out strats.