how can I make chapter headings in LaTeX become centered, without changing anything else? I have tried a number of things, but they have either not worked, or radically changed the look of the heading, or both.

That depends on the style file.

Search for a suitable style file on Internet or edit .....

Which file did you try to edit?

you might put this in the preamble (before \begin{document})

\newcommand{\cchapter}[1]{\chapter[#1]{\centering #1}}

then, instead of
\chapter{some title}

use
\cchapter{some title}


you could do the same with section, subsection, ...
(\newcommand{\ssection}[1]{\section[#1]{\centering #1}}, etc.)

How do I do this (i.e. center a chapter) if I have the following:



\documentclass[12pt,letterpaper,twoside]{book}
\begin{document}
\tableofcontents

\addcontentsline{toc}{chapter}{WEEKDAY EVENING PRAYERS.}
\chapter*{WEEKDAY EVENING PRAYERS.}
In the Name of the Father, and of the Son, and of the Holy Spirit. Amen.

more text

quite a bit of text, including several more chapters as above

\appendix
\chapter{ON THE SIGN OF THE PRECIOUS AND LIFE-GIVING CROSS.}

three more appendices

\end{document}


Thanks,
-Michael D

Have you tried this?

I recommend to use the titlesec package to achieve that, here's a complete example:
Stefan


--
TeXblog

How would I do this for section headers & subsection headers?

I tried the following, but got an error code.

\titleformat{\chapter}[display]
{\normalfont\huge\bfseries\centering}{\chaptertitlename\ \thechapter}{20pt}{\Huge}

\titleformat{\section}[display]
{\normalfont\Large\bfseries\centering}{\sectiontitlename\ \thesection}{16pt}{\LARGE}

Help, please.
-The Doctor

Try
Stefan


--
TeXblog

Thanks for the help Stephan. Only one more question, and that is how do I get the headings [chapter, section, etc] numbered in the toc, & yet unnumbered in the body of the text?

Thanks a lot for your patience & help,
-The Doctor

That seems to be inconsistent for me. Further, numbering supports browsing/finding sections, to follow the order of sections. While it's easy to read a toc and to have an overview of the order there, it's harder to find the way inside a document, that's why I think numbering is even more important in the document than in the toc. Or, to go further, do you show page numbers for chapters and sections in the toc, but don't use any page number in the document itself...? Numbering is not just counting in order to show how much has been done. I'm just thinking.

Such numbering is not a direct supported style (that tells something about if it's common), but of course you can achieve that. Use \chapter* and \section* in the document and use there also \addcontentsline (or \addtocontents) to produce a numbered toc entry. Use a counter, define your own counter or use standard chapter/section counters.
Another way would be to redefine internal macros like \@startsection, \@makechapterhead etc. but first be sure that you really want to use this style.

Stefan