To get your own place, you will likely need to pay (1) a security deposit (often the same amount as monthly rent) and (2) at least the first month's rent.
You can start thinking about whether you want to rent a room (where you share other rooms like bathrooms, kitchen, etc. with whoever else lives there) vs. studios vs. 1 or more bedrooms.
How much that costs depends on where you live. You can check out websites like apartments.com to search for options in your area.
So how do you save money? Read as much as you want on topics related to personal finance. Look at other posts people on this forum make regarding budgeting. Find other articles or books on personal finance topics that you want to know more about. Also, check out the links below.
Some other advice I can give:
Figure out how much money actually comes into your bank account each month.
Figure out your expenses each month.
Figure out how much is left over for you to save, spend as you wish, etc. If nothing is left over, then you either need more money, or fewer expenses.
You can think of "budgeting" as creating goals to do three things (1) pay your past debts (e.g. student loans?); (2) pay your current bills; and (3) plan for your future expenses (moving out, emergency fund, newer car, etc.)
Thank you so much!!!!!