How do I become an administrator of a deceased person's assets?

Evidently the car was still in his name when he died.  Therefore, it will be necessary to file with the probate court in order to get the car transferred into your name.  You should contact the probate court that has jurisdiction for the county in which he lived and ask about the proper forms to be filed for a decedent that died without a will and who left a small estate.  In many states there are streamlined probate procedures that apply to small estates.  Therefore, the probate process may be simpler than you might think.  You will need to apply to the probate court in order to be appointed administrator of your grandfather's estate.  Then you will receive the required certificate of appointment that you need to provide to the DMV in order to transfer the car.