I'll go into a lot more details about social customs in later sections, but for more general social rules, the Regency era was a time where politeness and discretion were held in high regard for the upper classes. Not only women, but also men were all meant to be modest, intelligent conversationalists, not prone to fits of passion one way or another. Men were almost all university-educated, while women were taught to dance, sing, play instruments, sew, write beautifully, paint, decorate screens, and run a household. They were also expected to learn French, German, and Italian, though not Latin or Greek, which men would learn in university. All this said, "refinement" was deeply important in upper class society.
This more rigid societal structure meant people were not supposed to be loud or rowdy, were meant to have taste in classical art forms and moderate forms of exercise, and treat one another courteously. Almost in amusing contrast to this is the baseline extravagance of the wealthy at the time, but that aside, I did want to highlight a few small things in this section - how introductions worked, calling cards, what a "rake" actually was, and how inheritance worked.
There were a couple basic rules with introductions. The first was that one was not supposed to introduce themselves to a stranger without a "proper introduction." In fact, without a formal introduction, people were basically supposed to act like the other didn't exist. An introduction in this society was a recommendation, basically, so accepting an introduction meant accepting a relationship, so people could refuse to allow someone to be introduced to them, but essentially an introduction almost always had to be done with a third party mutual acquaintance, though sometimes the host of an event would conduct introductions that night. Who was introduced to whom was also a matter of status. Instead of doing what we do, where we introduce both parties to each other, one person would usually be introduced to the person of higher rank, such as "This is my acquaintance Sarah Baxter, Mrs. Harper." Title and status was actually less important than age and gender. Younger people were introduced to the elders, while gentlemen were introduced to ladies, regardless of rank, though everyone was introduced to royalty (taken almost verbatim from one of my sources below). With any introduction or meeting of two people, ladies would curtsey, men would bow. Kissing the back of a lady's hand was a polite way for a gentleman to greet a lady, but generally not on their first acquaintance, and they had to be careful not to do it too long or passionately, lest it be considered a sign of intimate affection.
Visiting (or calling upon) friends, acquaintances, or to-be-spouses at their home was not at all an uncommon, but in the event of that happening, one was required to hand over a calling card when they arrived before they could be received. A calling card was a business-card-like piece of paper with one's name on it and (for men only) address, and this both announced one's presence and allowed the family to keep track of who they'd received and when.
If you have any familiarity with the term "rake," you might have a vague idea that it was about a guy people didn't like very much, or even a womanizer. Really, a rake meant a person who was overly indulgent (again, harking back to the importance of modesty), particularly with drinking and gambling. While it was true that men were allowed to "sow their wild oats" sexually to some extent (technically rake doesn't refer to womanizers specifically, there were other words for that), this could really only be done with girls of no consequence to high society - widows, prostitutes, actresses, and other lower class or "inherently" morally loose women. Even then, an indication that a man was indulgent, overly passionate, and wasteful reflected poorly on him to high society, and the term "rake" was really not a positive thing. This wasn't considered a biker gang leather jacket "bad boy," so much as a Karen in reputation.
As you'd probably expect, inheritance was based on male primogeniture, meaning the eldest son would inherit all titles and properties of his father, and if the person with title or land had no sons, the closest living male relative would inherit. Landholders were pretty much not meant to have any other work, but the younger sons were often supposed to find some sort of reputable work, mostly in the military, the clergy, or as some form of lawyers. Women, meanwhile, had no real prospects unless they got married or had relatives willing to provide for them, which was why it was so essential for them to make a decent match, not just for their family ties, but for their own future and the future of their sisters and daughters. This was especially difficult for an upper class family who had daughters, but no sons, because if the heir of the estate didn't like them or care for them, they had every right to throw all the women out of the house they'd lived in their whole lives the second the current holder died, especially if they were already married and had a wife to take care of the household affairs so that the widow wasn't necessary.
Various sources: To be an Accomplished Lady - Random Bits of Fascination ; Younger Sons in Jane Austen’s England ; Male Education in Regency England ; Regency introductions - a Regency History guide ; Introductions, Regency-Style - Donna Hatch ; The Etiquette of Using Calling Cards