Sunni Muslims, who are traditionalists of some sort, usually cite both the Koran and sunna as their sources of authority. The Koran is their scriptural text and sunna a term meaning “tradition.” The latter refers to the tradition established by Mohammed and the early generations of Muslims. Tradition is anything that’s recorded about what Mohammed said and did that didn’t make it into the Koran, but has been passed down orally and checked through what Muslims call “a chain of transmission”‘namely, that it comes from a legitimate source, such as the wife of Mohammed or a companion of Mohammed, and is considered, in a sense, revelatory.
Mohammed is regarded as the perfect man. When he speaks or acts under inspiration, it is as if Allah speaks directly through him, even when he conducts himself in jihad or when he’s ruling on domestic issues. Though not directly from Allah, it is inspired as well because he’s a prophet of Allah. Then later Muslim jurists fill in the gray areas, using deduction and analogical reasoning.
In the sunna there is also the hadith. There are a number of collections, some having more authority than others, depending on the chain of transmission. Then there are the Sira, or biographies of Mohammed, which date about one hundred eighty years after his death and are of questionable historical veracity. Lastly, some view other early accounts of Islam and the early Islamic conquests as authoritative in the proper conduct of Islam.