The graphic here provides a quick tip guide to the rules of introductions during the Georgian era.

Of course, it was more complicated than these four points. For example, gender before rank, age before gender, an introduction for a dance was not considered a formal introduction, etc.

Hands down the best post on introductions for your reading pleasure:

Regency History: Regency Introductions: A Regency History Guide

For a more complete break down when it comes to when and to whom to bow/curtsy, shake hands, nod, etc., explore this guide, complete with flow chart!

Golden Romance Research: Greeting Etiquette