Step 1: Inherit the family fortune, but only if you have to. Otherwise, start a lemonade stand.
Step 2: Get a part-time job that's not too embarrassing to tell your friends about
Step 3: Learn to cook something other than ramen
Step 4: Join the Peace Corp and earn a free passport while pretending to be cultured
Remember, financial independence is just a fancy term for 'living off of ramen noodles and your parents' guilt