That’s going to be theme-specific. If there’s a theme that you otherwise like, please link either your site or the theme demo and I can help you set up the code injection. Happily, you just need to do it once and it’ll apply to all posts. :)
I usually put styles in the header, although either will work. Don’t forget to hit ‘update’ after you add it.
For a less code-requiring solution, you could adopt the approach I describe here:
Perhaps you set it so that all headings that are set in the editor as italicized are actually centered. Or choose another styling option (or two) and overload them. Let me know if you need help figuring out the exact setup, but I think that’s an approach that’d make it really easy to center headers after you set it up (once, site-wide).