How should I save money?
So far all my earnings are going into my checking account.
If you're earning more than you're spending, then you're already saving money!!! :)
I was wondering is it OK to let all my money go into the checking account ?
The term "OK" is very broad. It's a heck of a lot better than spending it all on whatever frivolous thing people of your gender and culture know is "must have" at your age. But it's definitely not the wisest thing you can do with your money...
Or do I have to create a new bank account like a savings account and split the money in between ?
No, but that's a sub-optimal plan.
As I understand, savings account only yield like an extra $1 every year so is it even worth it ?
Most do, but there are many "on-line" banks, which pay a relative much higher (though still low) rate. My savings account is at Ally Bank, but there's also Capital One 360, Synchrony Bank, GS Bank and others. (They're real FDIC-insured banks, which just have a few branches and focus on Internet customers.)
so is it even worth it ?
Even if it paid trivial interest, I'd say that it would be, since it removes the money from your sight, so that you're less tempted to blow it.
Fortunately, because of on-line banks, you'll get higher rates.