My wife and I live in an apartment. There is a staircase right outside our unit, and everyday when I take him on a walk, I lead him up a few steps and then down again. He was pretty unsure at first, but with enough encouragement he makes his way down. He's 11 weeks now and just went down a huge flight of stairs with little hesitation!
They get used to it, but with my little guy, I think it was about size. He is now at a size that he can make each step in a stride, which makes it more comfortable. You might find the same with your pup!
Booker (Born 11/15/13)