Determine who is the executor of the will. If the will is written properly, the executor has been clearly named. Usually, the executor is a lawyer, law firm or a family member with some degree of legal experience. If the parent died without a will (called dying intestate), an executor may be appointed to carry out the functions of the estate and distribute assets accordingly.
Review the will to find out how assets are intended to be distributed. The executor is responsible for discharging all the debts of the estate appropriately. Current debtors receive precedence in asset distribution over heirs. The will may be unlikely to state how specific bank accounts are to be distributed, but the executor's status grants him authorization to gain access to all accounts belonging to the estate.
Contact the banks where the estate still has accounts. Inform the banks of the death. If the deceased had a joint account with a spouse, that spouse will still likely have access. Otherwise, the bank will temporarily close the account until the executor arrives with proof of her status.
Bring a copy of the document that names you the executor of the will of the deceased to the banks where the estate has accounts. This document grants the executor access to all accounts. You may then withdraw money from the accounts and close them accordingly.