How do I go about getting paid to care for my Father?

If your dad is a veteran check in with the Veteran's Administration. They have a program that pays a minimal amount to those providing care. There are qualifying guidelines.

You will need to ask your father how much he would pay you for taking care of him. If that is agreeable, you will need to draw up an employment contract stating number of hours worked each week, the hourly rate, and who will be paying the payroll taxes. Please note that a vast majority of grown children do not get paid unless their parent pays.