I make almost exactly the median income for my area at present. I manage to save about $200-400 a month. Some of that will be used over the course of a year for periodic expenses, like paying all my vehicle insurance in one payment instead of monthly (which gets me a discount) and vehicle maintenance, unexpected expenses, and so forth. I pay about $130 less than the median rent in this county (at least for now - we’ll see what happens when I renew my lease shortly).
Mostly, I just carefully consider any purchases I make. I don’t buy much, although when I do something like buy work shoes I spend about $140 on a pair, but that pair lasts me years instead of falling apart in a couple months (I took Vimes’ Boots to heart). My vehicles are fully paid for, a 2002 sedan and a 1999 pickup. I don’t much, but when I do buy I try to go for lasting quality rather than the absolute cheapest.
To be honest, though, quite a bit of my nest egg has been windfalls - like when the government sent us covid money that, still working full time, I didn’t really need, I parked it in a mutual fund that will be part of my hoped-for retirement. There have been a couple small inheritances.
But getting back to Sam Vimes and his boots - by valuing quality over cheapness there are many things I buy less often than many of my peers and over time that adds up. Most people don’t think that way, especially not in a culture than screams BUY! BUY! BUY! As part of that, I make very limited use of credit. I do have a credit card I use during the course of a month but it’s paid off at the end of the month because I hate paying interest. It’s a convenience, not an ATM. But that level of discipline is something I developed over time, it wasn’t something I had when I was 20.
Another thing is that I don’t desire some things my peers spend lots of money on - I don’t wear make up, I don’t purchase expense bath products, I don’t buy artificial nails, I don’t spend much on haircuts or styling. I don’t miss any of that, not really ever having desired it. Other women are quite different. Didn’t ever spend hundreds or thousands on extensive tattooing. I don’t buy an entire new wardrobe every season. Even when I had more money I never did any of that (no, I spent it on airplanes - so I am certainly capable of throwing money into the wind. Literally.)
And, like others have mentioned, I use my library a lot instead of buying books all the time (even if they are a favorite addiction) which is also useful for videos, too these days. I’ll go to the matinee/cheap show at the movies when I go to the movies, which is less than I used to. I’ve found a lot of ways in my life to be frugal without feeling deprieved.
TL/DR where I live it is possible for a single person with an average salary to save hundreds of dollars a month but very few do so.