How
You have the right to some confidentiality regarding your personal records while you are alive. After you die, you generally have no further privacy interest to protect. If your father were alive, you could not get a copy of his will unless he decided to show it to you. Once he dies, your dad's records, like his last will and testament and his death certificate, are usually public. The easiest way to get a free copy of your dad's death certificate, will and similar death records is from his probate file.
The Probate Files
Once someone dies, the law sets up a process for transferring the person's property and assets to the people named in a will or to close family members. This is called probate, and it is a court-supervised process by which the person in charge of an estate (the executor or administrator) collects the assets, pays debts and taxes, locates the heirs and beneficiaries and distributes the property to them.
If you were close to your dad, you may be named in the will as a beneficiary or inherit by law as an heir if there is no will. In that case, you know where the probate is occurring and probably also the name of the executor or administrator. You can simply call and ask that person to send you a copy of the death certificate, will, and any other death records you are interested in.
If you were not close to your dad, or if he died some time in the past and you were not involved in the probate, you'll need to track down the probate court and the probate case. Usually the probate file is opened in the state and county where a person lived just before he died. Check with family members if you have no information about where he last lived.
Once you find the state and county, visit the probate court there during business hours and ask the clerk to see the file. Provide your father's full name, date of birth and death and, if you have it, his Social Security number. The clerk will locate the file and allow you to look through it. You can review all of the death records in that file, and can even make copies for a small, per page fee.
Vital Records
If you don't want to take the free probate court option, write to the Vital Records Office in the state in which your father died. It's not always called Vital Records, so look under Department of Health if you can't find it. The Center for Disease Control's National Center for Health Statistics publishes an online document providing the information about where to look for vital records in all 50 states. It's called "Where to Write for Vital Records."
You can usually order a death certificate by going into the office in person, by mail or even online. However, it is not likely to be free. Most states charge a fee to get a copy of a death certificate.