-- Start a banking relationship. Most of today's college kids have checking accounts with ATM/debit cards attached, so they are familiar with how these work. If your daughter needs a new account, look for a no-fee or very low-fee account (some of the online banks offer debit/ATM cards and charge no fees). And understand the rules about overdrafts, particularly the fees associated with them.
She should also get a credit card and begin building her credit history. Again, a no-fee, low-interest card is best -- but urge her not to carry a balance unless absolutely necessary (explain the dangers of compound interest; make sure she reads the fine print to understand interest rates and penalties for late or missed payments). There are new rules about credit card disclosures designed to inform and protect consumers -- and you (and she) can read about them at the Federal Reserve's website (www.federalreserve.gov/consumerinfo/wyntk_creditcardrules.htm).
-- Start repaying student loans. If your daughter took out student loans, help her find out the mechanism for repayment and when repayment should begin. Like credit card debt, she won't want to become delinquent on a payment. By the way, if she's going into a very low-paying field, she might be eligible for a new program that lowers her monthly payments. (Check out here for more details.)
-- Help her learn about the financial markets. If your daughter is starting to save part of her paycheck, she should also become acquainted with the basics of investing. For example, the instruments (stocks, bonds, mutual funds and exchange traded funds), the concept of risk versus reward, and the importance of diversification and asset allocation. Don't expect her to become an overnight expert; you're really just sowing the seeds for further learning.
-- Remind her that she's in control of her financial destiny. Finally, explain to your daughter that part of being a grown-up is being financially responsible. Once she's gainfully employed, she's in control. She can choose to live within her means (or not) as well as choose to save for her retirement (or not) -- but she will have to live with the consequences.
I think most college grads (and even younger kids) are interested in personal finance -- knowing about money and how to use it is part of being an adult, and they're eager to be independent. Get your daughter started on these necessities and help her understand the importance of financial responsibility.
Being irresponsible can have seriously negative consequences; just as important, knowing how to handle money can really boost her confidence and help her achieve her life goals. And let her know, too, that you'll always be there to help her out with advice and know-how. Good luck!