Hi Ed,
Remember that if your friends and family decide to invest, they are investing in YOU, not your business. You will have to convince them that you can be successful in business, but ultimately their decision to invest if they do so will be because they believe in you personally.
Before approaching anyone for money, whether friends, family, a bank, or venture capitalist, you should (1) know exactly how much you are asking for, (2) know what you will spend it on, and (3) know when and how you will pay it back. You should put your agreement on paper, and be clear about what happens if your business is not as successful as you expect. If you won't be able to repay the loan if you business fails, then make sure the people lending you money understand that risk.
Maybe most importantly, only ask for money from friends or family who can afford to help you. Imagine, for instance, that you convince your parents to liquidate their retirement savings to invest in your business. If you fail or even take longer to pay them back than planned, it could severely impact their retirement and haunt you for years. People don't like to consider the worst-case scenario when starting a business, but it is important to be honest about that with friends and family.
Finally, you may also want to look for a mentor who has been successful in the same field you want to start your business in. While not specifically related to your friends/family question, mentors can increase your odds of being successful as well as introducing you to potential sources of angel funding outside your immediate circle.