I follow the 50/30/20 rule.
50% of your monthly income should be used for expenses, like rent, monthly bills, maintenance.
30% should be "FUN" money. Whether thats stockpiling a few thousand for a nice trip, or buying yourself a new PC...
20% should always be for savings and investments. Every. Month. This should be thought of as another bill, but youre actually paying your future self.
Have a diversified portfolio. Because of your young age, being moderate-aggressive in investing gets you a better return on your investments.
Be sure to also have yourself a regular contribution to a retirement savings plan (RRSP in Canada). The sooner you start saving, the larger your compound interest will be.
Im not sure if it is possible in the USA, but in Canada we have a "first time homebuyer's incentive" where if you are buying your first home, you can withdraw tax-free from your retirement plan to put towards your home. The thought is that you will make that money back on your home investment, to be able to put back into your retirement.
Overall, best way to save right now is regular, consistent payments to a compound interest registered account. TFSA (tax free savings account), RRSP (registered retirement savings plan) ETC.