Speak to an account representative at the deceased's bank and explain that you need to close an account. Provide the account representative with the name of the deceased as well as the account number and explain that the account owner has died.
Provide the bank representative with a certified copy of the death certificate and one form of your own government issued identification such as a passport or state issued ID card. If the deceased listed you as the pay-on-death beneficiary then the representative can close the account without requiring any further documentation. If you are the executor of the deceased's estate then you must also provide the banker with the letters of administration from the probate court that appointed you as the executor.
Tell the banker to close the account and to use the proceeds to purchase a cashier's check. The banker must make the check payable to the deceased's estate if you are the executor or to you if you are the beneficiary. Inspect the check to ensure no errors were made and then leave the bank.