If my dad is 77 and the only name on mortgage and title to house, how do we put my name on the deed?

This is not a task that a layperson should attempt.  Preparation of a deed and other requrired conveyance documents, and recording these documents on the land records should be done by a qualified attorney.  Your father will also need advice on such questions as: Is he going to convey the entire ownership of the hosue to you or does he want to retain an ownership interest in the property?  If both of you will be on title, will your shares be 50/50 or based on some other division of ownership?  If you will both be on title, does your father want title held jointly with right of survivorship or in some other fashion?  What are the state and federal gift and estate tax implications of the proposed conveyance?  Will this conveyance have any effect on the ability to claim the $250,000 exclusion from federal capital gains tax that may eventually be payable upon the sale of the house.  Regarding your last question: Conveyance tax is not payable in connection with a gift.

The bottom line is that you need a lawyer to prepare and file the documents; and you need some legal and tax advice on the questions mentioned above.