We started off holding his hands while he walked down the stairs. Usually he would hold onto the railing on one side and our hand on the other and go down like that. Then after a while, when he thought he could do it, he would refuse our hand and just go down holding the railing and we would be right next to him. Now, I usually got ahead of him (going downstairs) so I can catch him in case he falls.
What I found helpful to remember is that kids are naturally cautious, so if you let them go down the stairs, they will do so carefully because they don't like falling and getting hurt any more than you, but if you forbid it and they get a chance, in all likelihood, they'll be wreckless and hurried so they can do it before you stop them. And then, of course they get hurt. (John Holt talks about this in his books How Children Learn and How Children Fail). My son has fallen a few times (but I've always stopped him) but as a side effect, he has learned very well how to stop himself from falling when he loses his balance. For my part, Ive learned to let him decide how he wants to go down the stairs. Sometimes he goes backwards and slids down the flight very quickly. Most of the time he goes down walking holding onto the rail and on shorter flights of stairs he goes down without holding anything at all.
Oh, and we started this when he started trying to lunge down from our arms when we would be on stairs, which I think happened around the same time he started walking.