Installing carpet on stairs seems like an easy enough job. However, the task comes with step-by-step instructions that must be followed exactly in order to get professional results. Failure to address a few steps could be disastrous! The best word of advice I can give is: find a professional carpet installation guide and stick to it.
To lay carpet on stairs, you'll need tackless strips, stair nosing and treads, and of course, carpet. And this is just the beginning! To determine the list of tools you're going to need, you must first decide on an installation method: glue down, cap and band or waterfall. Cap and band installation is more traditional, but waterfall tends to be easier to lay down. Personally, I prefer glue down as I feel it holds the carpet in place better.
Once you select an installation method and gather all of the necessary tools and materials, you're ready to get started. If you come across any bumps along the way (literally or figuratively) make sure that you refer to the installation guide before attempting to address the issue on your own. Novice installers who are in a bind may want to consider hiring a professional installer to finish up the job.