How do I add a syntax highlighter format to Gedit?

Gedit (the default text editor) using GTKSourceView for it's syntax highlighting. It uses XML files to define how to highlight different syntax.

There is a tutorial and a reference document on the GTKSourceView site. Finished source file definitions are stored in /usr/share/gtksourceview-2.0/language-specs/ or /usr/share/gtksourceview-3.0/language-specs/, you might want to check them out to learn by example.

There is also a less in depth tutorial on the Gedit site.

After you create your new language spec, restart gedit and it will automatically add it to its list of languages.

I assume you are talking about gedit (labeled as "text editor" in the ubuntu menu).

Gedit is using GtkSourceView for syntax highlighting. You have to create a language definition for GtkSourceView.

Here is a tutorial: https://developer.gnome.org/gtksourceview/stable/lang-tutorial.html