This will depend on how far advanced the disease is and how ready your parent is to allow someone to help. You will want to make sure your parent has an up to date power of attorney for finances/property management. Preferably, this power of attorney will be done by an elder law attorney to make sure it has the tools that might be needed for benefit planning and asset preservation.
If your parent is still able to manage his or her finances, then you will want a system that allows someone else to at least check in by reviewing paper statements or online bank statements to make sure nothing odd is happening in the account and that bills are being paid. As the disease progresses, you may want to take over bill paying but keep your parent in the loop to the extent he or she desires and is able. Eventually, someone will need to take over managing the finances and the power of attorney document allows this to happen.