I remember a veteran carpet layer telling me a few years ago (when he was reinstalling new carpet on our stairs that the original installer had messed up a few weeks earlier) that anyone can lay carpet, but getting it right on stairways is where the you can see the difference between amateurs and professionals. Doing it right, getting all of the wrinkles out and hiding all of the edges would be a challenge for anyone.
If you insist on trying it yourself, get a good electric or better yet, pneumatic stapler (you'll also need a compressor for the latter). A good steel straight-edge is essential, as is a quality carpet knife (they're known as widow-makers for a reason, with double exposed sharp edges). Good luck.