The Ta`awwudh (تعوذ) is the phrase A'uzu billahi minashaitanir rajim (أعوذ بالله من الشيطان الرجيم), which means "I seek refuge in Allah from the outcast Satan". Muslim recite it before reciting Al Quran and usually before begining any task.
The Basmala (بسملة) is the phrase Bismillahir Rahmanir Rahim (بسم الله الرحمن الرحيم), which means "In the name of Allah, the Most Beneficent, the Most Merciful". Basmala may also be referred to by its first words, Bismillah (بسم الله). This sentence is recited before each sura of the Quran, except for Sura number 9 (At-Tawbah). Also, it's recited in daily prayers, and is usually the first phrase written in the constitutions of Islamic countries.