In addition to the tasks outlined in First Week, here are some of the key tasks you should be accomplishing in the first month.
Set up some file folders to keep things such as physical receipts, appraisals, bills of sale, death certificates, etc. It probably goes without saying, but license your copy of EstateExec from the estate's Overview tab.
Having a lawyer's help can be invaluable. They deal with this process every day; you've probably never done it in your life. That being said, many people opt to save thousands of dollars and handle things themselves. See Do I Need a Lawyer?.
State requirements vary from as little as 10 days to as many as 45. If a will cannot be found, the person will be considered to have died intestate, and state law will determine who has responsibility for administering the estate.
Start to collect information about estate assets (real estate, stocks, collectibles, etc.) and estate debts (mortgages, loans, etc.). This will likely take months to fully complete, as you gradually uncover hidden treasures and bills, but you can get a pretty good sense of where things stand by the end of the first month. See Taking Inventory for more details.
Part of your duty as executor during this time is to keep things running (businesses, households, etc.). For example, make sure any home is being maintained, and that the utility bills are being paid, etc. In fact, utility companies are notoriously aggressive about this, and missing a bill by a few days may trigger them to cut off services (try to avoid this). Please be aware, however, that you are not personally responsible for any debts, so if the estate will likely not have the funds to reimburse you, you should decide carefully whether you want to pay any of these bills.
If the estate includes a home that is now vacant or unoccupied, you may want to take additional steps to protect it, since such properties are more vulnerable (to theft, vandalism, squatters, broken pipes that go unnoticed, etc.). You may want to periodically check in on the property, and to consider hiring an alarm company, as well as a gardener to keep it looking lived-in. You should also be aware that insurance companies have special rules for vacant or unoccupied homes, and you may need to take action to ensure the home continues to be covered (see Consumer Reports and insurance considerations).
Cancel the decedent's cell phone service, Internet access, cable TV, etc. But don't cut off things like electricity or water!
The Social Security Administration (SSA) must be notified of the decedent's death, by calling 800-772-1213. You cannot do this online, but the funeral home may do this for you. See also SSA Reporting A Death.
Any social security checks for the month in which the decedent died, or later months, must be returned or repaid. If the decedent had been receiving Medicaid benefits, be warned that the agency will likely seek reimbursement from the estate.
See also First 3 Months.