Saving is much easier if you set a goal. Also have a checking and savings account. The moment you get paid, move at least 10% over to your savings and consider it gone. I mean don't even look at your savings account. Scrimp until your next paycheck. Whatever you have left right before your next payday also move over to your savings.
In order for you to set this goal you need to choose a price range for a car. First car should be a used beater. You can save a crap load of money buying used vs new. I can't believe I'm making the same speech my parents gave me 17 years ago but it makes total sense now. With your monthly income buying new is out of the question. Insurance, registration, and sales tax for a new car will hurt...especially insurance. Monthly payments for a new driver in his...20s? will probably cost you $100-$300 (depends on age, car, location, level of insurance...etc.). Gas will probably eat up $100-$200 a month if you don't drive too much. Factor in an average of $50 a month on maintenance for a used car.
So on your journey to car ownership keep in mind that just owning a car will eat up 20% of your paycheck minimum per month and possibly up to 40% of your paycheck. If you enjoy eating at nice restaurants and going out, owning a car can actually put a damper on that instead of opening up those opportunities.