If your company offers a 401k option, it's a good way to save. The company I worked for didn't match my contributions, some companies do and that is excellent. But I just put the most that I could afford out of my paycheck, and it was put in a basic savings account just a better interest rate than the bank, no gambling with stocks, etc. I've worked too hard all my life for my money, to throw it out the window. I know someone who lost a large amount of money that he let them put into his company stocks. When the company was thriving for many years, it was great...when the company started going downhill...not to funny.
Another way is to open a CD or IRA if you can find a decent interest rate. They're almost impossible to come by nowadays, but is better than a typical bank savings account. I save my change and pennies too separately. When I cash in my pennies, even if it's a small amount of money, it goes into savings. A coffee can can hold quite a bit of pennies.
I buy bulk at Costco, even though it's just the two of us. I vacuum pack the stuff into smaller portions and store like that. You can save good money by not buying everything at store prices. I use coupons when I can, and always look for sales. A penny saved is a penny earned, that was always a good motto to go by. My mom used to drill those things into our heads as kids, because we were far from rich. Money doesn't grow on trees, another commonly heard in my household, lol.
I don't use credit cards very often, but when I do, like for vacations or big purchase items, I pay it off in full to avoid those huge interest penalties. If I can't afford to pay it off in full, I don't buy it. Living within your means is even more valuable as we get older.