I inherited a 1/3 share of a farm that is co-owned by two other relatives. I sold the property for $76K. Do I pay income tax on $76K or only if it's sold for more than it's appraised for?

Your cost basis of the property is more than the fair market value at the date of death. If you sold for price more than you cost basis you have a gain. Report on schedule D/F (Form 1040).