I started saving from the moment I took my first part time job during school holidays and weekends, probably aged around 13. I started off doing room cleans/bedding changes in a nearby guest house at weekends and school holidays, spent my wages every week (clothes, magazines, going out etc), but saved my tips in a post office savings account. A couple of years later, I started waitressing in a nearby restaurant a couple of evenings per week - again, spent my wages but saved my tips. My tip savings account was "untouchable" in my mind - I just enjoyed watching it grow by small amounts week by week, plus interest being added, and of course, it grew a lot more during Easter and Summer holidays with a lot more tips! I had a fair amount saved by the time I left school, probably several hundred pounds which was a lot back around 1980ish and equivalent to a few thousand in today's money.
I then got a full time job but it was menial/very low paid work, less than £1 per hour, but it was a training job and had good prospects, so that was fine. I kept my weekend cleaning/changing job and also a couple of nights waitressing. I "Lived" on the wage from the day job, but then saved all the weekend/evening wages along with the tips, so the savings account started growing a bit faster. Still religiously not making any withdrawals and watching it grow week by week, made better by relatively high interest in the 1980s!
Eventually, I worked my way up in the firm and could afford to stop doing the weekend/evening work which had become hard as I was also self studying accounting exams in the evenings and weekends. But as my wages were higher, I started spending half and saving half. Savings started to build up even faster. My being strict, I just "lived" within my means, just like I'd been doing when part time at school - I gave myself a fixed sum to live on and adjusted my spending accordingly which meant I adjusted by buying clothes some weeks but going out more other weeks, and having a meal out only every few weeks - all depending on what I wanted to buy/do week by week - if I wanted a "big ticket" purchase or evening out, I'd do/buy nothing else that week.
This was all before credit cards and store credit became a big thing, so to an extent it was easier to live within your means as the temptation to put stuff on credit wasn't as easy.
By the time I came to get married and buy a house, I had around £35k saved, accumulated over around 15 years of small but regular savings and self discipline not to withdraw anything.