I’m going to be very frank- it is not particularly easy to start saving. Most people need to have it within them to start saving money, or they will be spenders for the entirety of their life. It might be too late for you, but there is a chance your kids could be big about saving money when they grow up. All you have to do is encourage them into saving some money from a very young age.
You are probably giving your children some pocket money. What I did with my daughter was I started giving her a tad bit more money than I thought she would spend, and started encouraging her into saving the money she had not spent at the end of the week. I also followed a weekly pocket money schedule, because I felt like she might feel the compulsion to spend more money if I gave her 30 days to buy whatever she wants.
I also started a bank account for her, and made sure she knew exactly how much money was going in there. She was rather happy to realize that there was a significant amount of money in an account- money that was only hers. Of course, I would also let her buy something special for herself once she had saved up enough money- something that was kind of expensive, but would not require all the money in the account.
She’s not old enough to be earning right now, but I’m sure she will be much better at saving money than I ever was.