They should give you an opportunity to look over the equipment and ask any questions about their use before you have to actually demonstrate your ability to use the stairchair.
Basically, the chair opens up, similar to a folding chair. You sit the patient on the chair and then apply the seatbelts/straps that are there to help keep the patient in position. (Typically a lap belt, shoulder/chest straps, and a strap that goes around the ankles to help keep the feet in place.) There may also be a strap to help hold the head in place, depending upon the type of stairchair it is.
The chair will have wheels on the back legs. Once your patient is secured, tip the chair back and move it near the staircase. It will take two people to get the stairchair up/down the staircase. One person is at the back of the chair, and one at the front. If there are handles that fold down/slide out/etc, you will want to make sure they are in the proper position. (Some stairchairs also have a track that looks similar to the tracks on a bulldozer. The track is on the back of the chair and folds out and locks into place.)
Tip the chair back and move the chair along the staircase. If you are lucky enough to have a chair with the tracks, lean the chair back far enough so that the tracks are making contact with the edges of the stairs and let it do the work. You will just have to control the speed and direction in which the chair moves. If you don't have the tracks, you will have to physically move the chair along the stairs.
I am sure if you look on youtube you can probably find videos of people using stairchairs. Also try looking up Stryker's website and see if they have anything there. Hope that helps, and good luck with you interview!