The main criteria for a hadith to be strongly authentic (Saheeh) is:
Itisal Assanad, that a narrator narrates from his sheikh/teacher/the person being narrated from and has been in his time and has met him, even if he had met him once
That the Narrator be righteous and pious, and Adala (العدالة) has it's requirements
That the Narrators be perfect in accurateness, both accurate in memory or in writing, or both if the level of perfectness of a narrators accurateness lowers, then the Hadith would become Hasan
That there is no Shudhudh (شذوذ), meaning that a trustworthy narrator does not contradict those who are more trustworthy then him
That there is no deficiency (علة) that would make the Hadith rejected, meaning thee narration must be free from (العلة القادحة) and there are types of Ilal (علل).
Those narrators who are not righteous then their narration would fall under Mawdoo' or Matrook. Those narrations which have a (علة قادحة) the authenticity will change. Those Ahdeeth which do not meet the above are not narrations which are Saheeh, and the ruling on it's authenticity will be ruled accordingly.
For further information, see this (Arabic).