Saving money can be tough, frustrating, and doesn't always work out. Don't feel bad because you're having trouble with that!
Personally I've found that splitting my income has been the most beneficial method of getting savings going. The more I avoid see the money I'm saving, the better I do. To achieve this I've opened a checking & savings account separate from my normal banking and deposit a portion of my paycheck there each month.
Coming up with a realistic figure of your spending however is key. Some things are set in stone such as any payments you're making (car, rent, etc) but for things like food, gifts, splurging you might feel that some $/month will suffice but learn it doesn't later. Take what you feel you can go without and hide it away from yourself in whatever method works best. Out of sight out of mind.
Start slow and ramp up if you can, and the path get rocky and you need to take money from your savings that's okay!
You are wise to be thinking about saving. Good luck.
Very good question that many people ask at all ages. When I was growing up, my mom would get her weekly paycheck and tell me that she had to pay herself-- as I got older, I realized that for part of each pay check, she put into a savings account for her future self. As I got into high school, I started being more social and spending money on the movies/clothes/etc and also wanting to plan for my future-- so I ended up getting my first part time job for extra money. If you haven't already, look for an easy entry level job-- bagger at your grocery store, sales associate at a clothing store, hostess, etc. and don't forget to "pay yourself". Instant gratification can be nice (ex: you make $50 from working a shift then you spend it the next day on a nice pair of jeans) but when it comes down to it, even part of that $50 could be used towards a car or something bigger that you will need for the future. Other answers here have mentioned "wants" and "needs" and this is where growing up comes into play-- you may "want" that new pair of jeans even though you already have a few pair at home, but maybe you "need" a car in the future.
Keep track of your spending
Separate WANTS from NEEDS
Avoid using credit cards to pay your bills
Put away cash monthly.
Check your insurance policies. Can money be saved each month?
Check other monthly services-- can you or downgrade to save?
In all seriousness learn about Bitcoin. If you save dollars you'll never get ahead because prices are rising so fast. You need to save in a money that they can't keep printing more of.
A very easy way to get started is with the Fold App. It's basically rewards card but instead of 1% cash back or airline miles, they give you small amounts of bitcoin back. As Bitcoin becomes more popular and the market value increases, you'll see your purchasing power increase rapidly.
Saving in a money that is appreciating in value instead of decreasing will likely make you change your spending habits and you'll begin saving even more over time.