say you have a table with columns
fldPersonID auto_incrementing primary key
fldFamilyName
fldGivenName
then to duplicate the row with fldPersonID = 5 use:
insert into tblperson (fldFamilyName,fldGivenName)
select t.fldFamilyName,t.fldGivenName
from tblperson t
where t.fldPersonID = 5
and the newly inserted row will be allocated the next auto_incrementing value for fldPersonID.