Sorry to hear about the old lady you were looking after John. a lot is dependant if she died at home under a doctors care or in hospital. I the case of being under hospital care you contact the bereavement officer in the hospital, they will give you the information you require, if under care from a doctor, then ask the doctor for details of the way forward.
I do not know of your situation with regards to the old lady and her son that is under nursing home care, do you have power of attorney at all or are you listed as an executor? If not her son would have to deal with the situation with your help.
You will have to deal and inform loads of people, whoever you contact ask to speak to the bereavement office, be it the local authorities, her bank, insurance companies etc.
As others have said take your time and do it all one step at a time.