Can anybody guide me in rewriting a commit in Git?

I have this Git repository on my computer, and I’d like to do another push to the central server. However, I made a mistake in one of the files in a previous commit that I cannot publish online. Thus, I want to rewrite that commit.

However, I tried doing it on my own using the Git manual, but I didn’t manage. So Fluther is my last hope – can anybody (e.g. through PM’s) guide me through the process of rewriting history?