Budget! Keep a record of all your spending: bills (phone, car, insurance, etc.), necessities (food, gas) non-necessities (clothing, dining out, movies, etc.); and your income. When you have it all down in writing you'll be surprised how much money you spend on the non-necessities like eating out, shopping, small day to day purchases.
Decide how much you want to save and how much you'll need to put aside each month to reach your goal in a designated time period. It's a good idea to open a separate savings account and deposit a portion of each paycheck that will be set aside for your moving out money. It's also helpful to decide how much you'll allow yourself to spend each week on the non-necessities and do your best to stick to it. Good Luck!