R has Alzheimer and my father passed away in Jan of 2015, I am my mothers 24/7 caregiver and live in the home with her my question is she has been talking of adding me to the deed what does that entail and how is it legal especially with a mortgage?

Is your statement "My mother has Alzheimers?"
Your first step is to contact the bank who holds the mortgage to get permission. They may allow it without much fanfare if most of it is paid. If yes, you and your mother go to the deed office and add your name and pay a small filing fee. They will tell you the wording to make sure that you have 'survivorship.'
If not, they can make you apply to qualify. Make sure there isn't a life insurance policy with the mortgage, if in your father's name! Often there is one.
A better step is for your mother to have a lawyer write a revocable trust with you as the beneficiary. That way, you get the house without waiting for (or paying for) probate when she dies.
Also get all the kinds of POA you can get while she is alive, if you don't have them already.
Also have her sign and approve an advance directive for her medical care.
The lawyer will do all this at once, and it's easy so shouldn't cost much.

Frankly, this is going to be difficult. Depending on how far advanced the Alzheimer's s, she may not be considered competent enough to sign a deed. There is also the question of how the property was deeded prior to your father passing away. Were they joint tenants with right of survivorship? Was the property transferred to your mother?

The mortgage lender has to agree to the transfer or they can call the mortgage. They will probably not agree unless you agree to be responsible for the mortgage. There is also the issue of whether mom has a valid will or has given someone power of attorney.

The general process is have the property owner sign a new deed conveying ownership from them alone to you and them as joint tenants. But, especially in your situation, its not that simple. I strongly suggest consulting with an attorney.