There is nothing that demonstrates the change in etiquette over time like the etiquette around bodily functions. To a great extent, this is because of practicality. It is only the technology that allows us to distance ourselves from our excretions that allows us to be squeamish about them, in the past they were a fact of daily life that people had to see up close.
For example: during a dinner party, once the men and women had separated, a man might pull out a chamberpot and use it without even breaking the flow of conversation.
What did people use?
There was actually quite a variety of privies (what toilets were called). Some London houses had a kind of toilet like we have today, with water that flushes the waste. However, they didn’t have the technology to trap the smells, so they could be a bit unpleasant. Some homes had ‘earth closets’ which used a fine dirt to contain smells.
Most common people used a privy/outhouse, a hole in the ground with some kind of seat over it. These emptied into cesspools, which were ideally emptied regularly by “night soil men,” but in poorer areas, they were allowed to overflow and were a large contributing factor to disease.
Of course, at night, you wouldn’t want to go too far from your warm bed, so people would use a chamberpot. A chamberpot is a bowl or container (as plain or fancy as your circumstances would allow) that is kept under the bed (or sometimes in a special stool to conceal it and provide a seat) to be used during the night. You (or your maid) would empty it in the morning.
But what about when you were out and about? Many places didn’t have public toilets back then, so a well of lady would travel with a bourdaloue, a very small chamberpot that she could discreetly put under her skirts and then hand to a maid for disposal. Of course, men could always use a handy wall or alley.
How did they go?
If you’ve ever helped a bride to the bathroom, you know that it can be difficult to maneuver when you are wearing a fancy dress. However, we have difficulties because we don’t do it every day! Women in the Regency period didn’t wear underwear (well, they didn’t wear confining underwear like we do), so they didn’t have to futz around under their skirts. And with a chamberpot, you could just move it under you rather than trying to fit yourself around a stationary toilet.
For wiping, there might be scrap fabric, moss, or straw. That one ply toilet paper in public restrooms doesn’t seem so bad now, does it?