How can I add in the regular expressions for an additional syntax language?
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-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