My #1 tip is don't carry the bike up on your shoulder etc- if you lose balance, you're screwed. Keep its center of gravity lower than that, and don't have its weight up-hill (up the stairs) from you, so if you lose grip, it doesn't tumble back down and knock you down the stairs.
So I try to sort of walk side-by-side with the bike, one hand gripping the headtube/stem are or the front wheel (rather than handlebar/grip) to keep things centered, one on seat-tube or where seat tube meets the top tube for the majority of the lifting.