How do you get a probate court to appoint an executor of a small estate?

Not really an "estate" like a rich person has, it's just we're trying to get the money for his burial from the insurance company and they won't do it without having an executor named.

I just need to know the steps and what to expect.

I served as the executor to my brother's estate, but he appointed me in his will. Most of the time I worked on the estate by myself, as we had an incompetent attorney. The main help that I received was from a book that I bought on how to probate an estate, but I could have checked it out of the library. It has all the forms that need to be filled out. You may need to go to court to have someone appointed. Call the county probate court where this person died and ask them how to have an executor named. If they won't tell you, then you will need to get a book, look online or hire an attorney for advice. There may even be a kit that you can purchase at a store like Staples. It should not be a major expense to consult with an attorney for an hour, but be organized, have all our your questions ready and the forms filled out that you feel are necessary. He can look them over. If you do not have the money to do this check with legal aid in your area. Once you have filed the appropriate forms in probate court, you can then apply. Good luck. It is easy if you follow the forms.

You (or your attorney) have to file a petition in probate court requesting an executor be named. (The rules for this vary from state to state, you'll get a better result if you hire an attorney for a few hundred dollars.) All potential heirs who have a say in the estate are served notice that a filing has occured, and they are given the date of the one court appearance after the filing and then the executor is appointed.