to clear a room you mine this leaves a floor and ceiling.
For stairs up/down stairs allow you to go up or down from the layer they are on. This requires stairs on the layer you are moving to as well. Down stairs go only down up stairs go only up.
To remove the floor from a layer you would use channel, this leaves a ramp on the lower layer that allows movement up and down. These can be removed.
to mine a stairwell you need to press m, t then select the square and move up or down however many layers you want to go and then click again, that will designate those blocks to be cut into stairs (it will show the stairs but they will not actually be stairs there until a dwarf does the mining). This will designate a down stair at the top layer you select and an up stair at the bottom with up/down stairs in between. you need to have a dwarf assigned to mining to do this.
You can build them in the construction menu as well but that requires you to have already mined out the area you are building in so it takes longer.
If the above doesn’t work post a screen shot of what yours looks like.