Sometimes when I get home from work, my wife says "I went shopping today. Guess how much money I saved?" I can only wonder how much money was actually spent to obtain those savings.
You can "save" money by looking for the best deals shopping, but if at the end of each month you're still broke, you are not "saving" anything. Saving money is really about contributing to a savings account or retirement fund that progressively grows over time. It doesn't matter how efficiently you spend money, if it only lasts until your next paycheck. There's no difference between living day to day, paycheck to paycheck, or month to month. In all of these cases you are not actually saving anything.
Contributing 10% of you income to a 401k, a Roth IRA, or to a savings account is considered the norm for saving. Take a moment to understand how much that is. [Move the decimal point once to the left on your paycheck]. That is the amount of money that should be divided up among your various savings vehicles.
Getting some people to set aside money, and not touch it, can be like pulling teeth. My Motto is out of sight, out of mind. Set up an automated 10% deduction from your paycheck. After a little while you won't even miss it. Next keep the money with another bank or somewhere that makes it inconvenient to transfer money back into your checking. That way you won't be tempted to replenish your checking account when you overspend.
Even if you continue to live paycheck to paycheck shopping for all the best deals, you will be secretly be saving, and that's all that matters.