Adjust to the new reality
Parents and children may view the college graduation as two different things. For your child, it is definitely the beginning of their life, and unfortunately can be a difficult transition to adulthood and responsibility. The parent, while understanding what the child needs to do, may not fully comprehend what a challenge it can be. More importantly, the parent often will view the college graduation as the end of their life filled with responsibility, and may be over anxious for their child to make their mark in the world.
This is another excellent time for both the parent and the child to talk about expectations, especially if the child has come home to live after graduation.
For the parent
Try and be both patient and helpful, while setting certain limits for the child. For example, while it may unreasonable to expect your child to come in the house when it's dark or go to bed at 10 p.m., it is not unreasonable to expect that they will start earning their keep. Even before they have a job, responsibilities around the house, and doing for themselves will be an excellent teaching tool. After all, they need to be prepared to go out into the world alone.
For the child (now an adult)
You've hopefully had a great time at college, and feel like you could take on the world at this point. Understand that there will be plenty of reality checks in the coming days, weeks and months as you begin to fully appreciate that the party is over! Don't be overwhelmed by your new responsibility, but at the same time don't shirk it. It is now time to begin your adult life, and that begins with acceptance of the challenges that lie ahead: a job, a place to live, paying bills, and all of the financial planning steps laid out in this website, including debt management, budgeting, insurance protection, retirement savings, etc.