More important than the amount of money you save is the consistency with which you save it. Obviously, people who are wealthy and can afford to save large sums of money are going to benefit from larger interest earnings, but for the rest of us- even saving a few dollars on a consistent basis is going to add up over time.
Money is worth more the longer you have it, especially if you are saving it in interest yielding accounts. The local bank has savings accounts, and there are numerous providers of high interest savings accounts online that can really maximize the money you are saving to help it grow.
One way to establish a disciplined savings routine is to use an automatic deposit service. Whether you go with a retirement or investment plan through your employer, or set up a savings account that is automatically fed with transfers on a certain day of the week from your main bank account- its important to establish a regular savings plan. First, determine how much you can afford to save- and dont say, NONE! If you really feel you dont have any money to save each week, start with a very small amount, such as $3 a week. I guarantee you wont miss the $3 a week...