The Improbable Stair exists everywhere there is something to exist. It winds through all the Secondary Realms, through time and space, and through the House. It can only be opened by a Key, or other extremely powerful instrument (such as the Piper's pipe, the Mariner's harpoon, etc). The wielder then has to imagine that there is a stair made of anything they can see, and take the first step onto it.
The Old One tells Arthur: 'Once upon the stair, you must keep going until you arrive where you want to be. The Improbable Stair has many landings, and upon each landing you may need to find the Stair again. If you do not find the continuation of the Stair quickly, you will be stuck wherever and whenever you have stopped.'
To access the Stair again, the climber had to visualise it again. At first, Arthur had to make drawings or other things that looked like stairs. However, he gradually become more proficient at accessing the Stair without the need for props.
In Sir Thursday, it is stated that the Stair rejects most Denizens, though it will always accept Piper's children.