When my eldest boy starting doing potentially dangerous things, like climbing up all manner of things, I had to make a choice. I could try to stop him from doing it, or I could teach him how to do it safely. Ultimately, I knew I wouldn't be able to stop him, so I took the second choice. I was so glad I did.
At a playground I encountered a over-protective mother that wouldn't let her daughter climb anything more than two feet off the ground. My boy at about the same age was like a monkey, totally confident and able footed. When the over-protective mother turned her attention away for but a moment her daughter was up high and stuck. She couldn't get down safely and looked quite clumsy. She became scared of the height and almost fell several times.
My monkey boy ended up being the saviour of the day. As the equipment was designed for kids, it was difficult for me to climb up safely, but I gave it a go. The other mother was too scared to even try. By the time I got half-way up my monkey had made his way over to the girl and showed her step-by-step how to get down. When she got to me I decided to just hold back and let my boy show her all the way down, remaining ready to catch her if need be. She got to the ground without any further problem.
Her near paniced mother praised my boy's climbing ability and commented that her girl wasn't a good climber. I just explained that he just has more experience because I let him learn how to do it, and maybe her daughter would do better, and be safer, if she had more practise. The following week I saw them there again, and this time the mother was proudly coaxing the girl to carefully climb safely, a little bit at a time. By the time our kids were in kindy, the girl could climb as well and as safely as any other kid there.
Be it stairs, play equipment, trees, or whatever, I recommend that you would be better off teaching your child as soon as she starts taking an interest, and give her lots of practise until she can do it safely and well. Otherwise, she will do it anyway and get herself into a world of hurt.
As for getting down stairs safely, one stair at a time on their bottom works well, or if she is too inclined to stand up and tip forward, crawling down backwards works too. If you have a bannister she can hang onto, get her using it.