I do a lot of things to save money, but the thing that I think has helped the most is to avoid going to the shops unnecessarily. It's so easy to go to the shops and see such lovely cheap items that you might want but do not need. Or pop in to buy some milk but then see chocolate biscuits on special and end up walking out with a dozen items. I am very mindful these days of what I do purchase and have a good think about whether it is necessary or not. Even if it's only a few dollars, that adds up over the course of a year.
I think there's a few things but I think it boils down to monitoring your spending and having some goals in mind for what you are saving for. An end goal can help you to visualise why you are saving money in the first place, and by looking at what you are spending your money on you can identify any bad habits and improve on those.
It can be a good idea to look at your every day spending and see what it is you are spending all of your money on, and where savings can be made. There is a lot of incidental spending that occurs and it's amazing to see how much you've been spending on take out, or coffees. Simple changes like making your own lunches can make a difference.