How to file for executor of an estate of deceased grandparent with no will?

Please give my condolences to your stepkids on the loss of their grandfather.   If he had no Will and there are no living children, then your stepkids will need to figure out whether there is anything in his estate and, if so, they will need to decide whether they want or need to open the estate for administration. They should try to gather as much information as they can about what he may have owned and what debts, if any, he may have had. If there is real estate, then they really do need to try to deal with the estate in some fashion. If not, then they may have the option of walking away if it looks like there isn't much there. They really should get a consultation with a probate attorney- opening an estate for administration and dealing with it is not necessarily that difficult a process, but it is one that has potential pitfalls, and having the assistance of an experienced probate attorney can be very helpful.