It depends upon how the property was titled at your dad's death.
If the property was titled as joint tenants with right of survivorship, the title transfers to your mom by operation of law, and you would ordinarily record a certified copy of the death certificate along with an affidavit establishing that the person named in the death certificate and the person whose name appears on the deed are one and the same person, in the real property records. This makes it clear on the face of the public record that the transfer by operation of law upon his death has occurred. It would be better practice to pay the quite low price an attorney would charge to make sure that this is done right.
If the property was titled as a tenancy in common (which is true unless the words "with right of survivorship" or "JTWROS" appear on the face of the deed placing them in title together), then the ownership of your dad's undivided percentage ownership interest in the house must be done via the probate process which is governed by his will, if he had one, and by the laws of intestate succession, if he did not have a will. The person named in a will, if there is one, would have priority to be named as executor, and would seek that appointment in a petition filed with the appropriate court in Florida with probate jurisdiction. If there is no will, your mom is probably the person with priority to be appointed, but can waive that in favor of her children (any sibling with have to waive priority or be jointly appointed). Once the executor is appointed by a court and issued a document called "letters", they execute an executor's deed (which is a special form) from the decedent to the person entitled to inherit it. Either way, you should have an attorney handle the probate court filing.
It is highly desirable to clear up the record title in one way or the other, as this must be done before any sale to a third party and before any new mortgage is obtained, it will simplify inheritance at your mother's death if she still owns it at that point, and it will prevent property tax bills from being issued to your deceased father potentially creating a complicated probate case. You should also have the house appraised as of the date of his death as this value is relevant if the house is sold prior to her death for capital gains tax purposes.