The simplest way to do that would be by using server side includes...
1. Save your pages that will have includes with .php extensions (servers don't normally parse php in .html files, but you can do that, pretty easily, if your hosting company allows it)
2. Create an empty file that will have only the code of the item(s) you want to include. For example, if it's a group of links, the file will only have the <a href=... code and text for the links, no <html>, <head>, <body> or other code that normally appears in a full page. Includes are just fragments being added into the page, not complete pages.
3. Save that file into an includes folder in your site for organizational purposes...
includes
header.php
navigation.php
text.php
4. Add a php include statement into the code of the page that you want your server to add it to, where you want it added. The server will replace the include statement with all code from the include file, so inserting it in the correct location is important. With the above folder structure and example pages, the include statement would something look like...
<?php include 'includes/navigation.php' ; ?>
Wherever you put that small snip of code, all code from the navigation.php file will be written in its place.
5. Upload your pages and include folder to the server. As long as you have PHP installed (most servers do), the include's file will be written into every page that it appears on, automatically when your viewers pull them up. If you ever want to change something site-wide, all you need to do is update and upload the include file. The server will push your updates automatically to every page that has a given include statement.