Allaah says (interpretation of the meaning) in Quran:
"Eat not (O believers) of that (meat) on which Allaah's Name has not been pronounced (at the time of the slaughtering of the animal)"
And the Prophet (peace and blessings of Allaah be upon him) said:
"If the blood flows and the name of Allaah is mentioned, then eat." So in order for the meat to be halaal, it is essential that the name of Allaah be mentioned.
It is also mustahabb to say takbeer, so he should say: Bismillaah, wa Allaahu akbar (In the name of Allaah and Allaah is Most Great).
Al-Bukhaari (5558) and Muslim (1966) narrated that Anas (may Allaah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) sacrificed two horned black and white rams. I saw him placing his foot on their sides, and he said the name of Allaah and he said takbeer, then he slaughtered them with his own hand.