The "Water Ladder" is a structure to facilitate quick climbing in a strictly vertical manner. The accessible portion of this structure is a 1x1 shaft, but if created above ground would require 3x3 blocks of horizontal space.
Structure
The ladder is essentially two shafts separated by a wall. At the top of the second shaft, a water source block is placed. The ladders are placed, much as they usually would be, every other block. However the placement here is important; the first ladder must be placed in front of the hole leading to the water source block.
For every two blocks dug down, dig two blocks over and then one up to connect the water shaft. Place ladders in front of all of these openings to stop the water from flowing out into the ladder shaft.
When completed, the water permits the user to climb faster than if just climbing ladders.
Ladders vs. Signs
It has been noted that this phenomenon can be achieved by placing signs in front of the water outlets as well, but if the water ever is stopped, you can't climb signs back out.
Another reason to use ladders rather than signs is resource efficiency. It costs 7 sticks to make one ladder, equal to 3.5 planks, while a sign is comprised of 6.5 planks. Ladders also stack in your inventory, so you can carry more of them, or have room for other gear.
However, transport down is faster when using signs, one can simply fall down the shaft and then land on a pool at the bottom. When using ladders, you'll have to climb down.
Notes
Due to the South/West rule, only water ladders facing south or west (user facing the water) will work.
Hidden Water Ladder
It is possible to make a hidden water ladder. To construct one, build your water shaft normally except put dirt or cobblestone where you would normally put the ladder. Then, move one space sideways, and dig a shaft upwards there. Face the corner where the water is and press up. Voila! Now hide your water source blocks and you're done. Using his method you can remove the usage of signs or ladders, but also makes it difficult (not impossible) to go downwards without damaging yourself, so this type is ideal for one-way up shafts. The other downside is that it only works when it is facing southwest (user facing the ladder).
Resources
There are a couple videos on YouTube featuring the speed of a water ladder and also the creation of one.