Per IRS Publication 551 Basis of Assets, page 8:
To figure the basis of property you receive as a gift, you must know its adjusted basis (defined in IRS Publication 551, page 4) to the donor just before it was given to you, its FMV at the time it was given to you, and any gift tax paid on it.
The cost basis would depend on whether or not the fair market value of the property is less than, equal to, or more than the donor's adjusted basis. Please see the publication for details.