The word Islam means submission or surrender, and the word Muslim means one who submits or surrenders.
As the prime teaching of Islam, Muslims believe in one god called Allah (which means god). They believe he is omnipotent and omniscient, but they do not believe Allah is a trinity (cf. Koran 5:73).
The sacred text of Islam is the Koran/Quran/Qur'an (which means the reading). They believe it to tbe the word-for-word revelation of God as revealed to Muhammad. It contains 114 Suras (which means something enclosed by a wall). Each Sura is named after something or someone mentioned in one of its sections (called ayahs), and they are generally ordered from longest to shortest. The Koran contains Islamic theology, history, moral teaching, etc.
Muhammad was born in Mecca around AD 570. He is considered by Muslims to be the last prophet of Allah, and was given the Koran over a period of 23 years in order to restore the true, uncorrupted Abrahamic faith. If the doctrine of Allah is the prime teaching of Islam, then Muhammad as Allah's greatest prophet is next in line. Muhammad's basic message was that the only true religion acceptable to Allah is complete submission to him.
According to Islam, no sacrifice is needed for forgiveness of sins. Instead, forgiveness comes through belief in Allah, repentance, and adherence to the ways of Islam.
Islam teaches that Jesus was a great prophet, but nothing more. Muslims believe that calling Jesus God is the worst of all sins, called Shirk. Shirk means essentially polytheism, and since Muslims reject the Trinity, they believe that calling Jesus God is professing polytheism, which goes against their prime doctrine of Allah. Shirk is the unpardonable sin of Islam, and those who believe Jesus is God will not be allowed into heaven (cf. Koran 4:48 and Koran 5:72)
The Hadith is another text of Islam, which they believe was written by Muhammad's companions and contains inspired principles and applications of Islam, though it is not the direct word of Allah as is the Koran.
Sunnis and Shiites
Muhammad established Islamic rule in the city of Medina, in the west side of Saudi Arabia, in AD 622. When Muhammad died, someone had to take over as religious and political leader. Sunni Muslims (the word is a reference to "tradition") believe that the rightful leader should be elected according to ability. This is what happened historically, and Abu Bakr became the next leader. About 85-90% of Muslims are Sunni.
Shiite (or Shia, meaning a group of supportive people) Muslims, on the other hand, believe that the leader should be appointed more directly, either as part of Muhammad's family, as directly appointed be Muhammad, or as appointed by Allah. Shiites believe that the rightful heir was Ali, Muhammad's cousin and son-in-law. Shiite Muslims do not submit to the rule of the Sunni leaders.
Sunni/Shiite religious differences
Though the initial difference between Sunnis and Shiites was political, religious differences have since evolved. Shiites believe that the rightul Imam (the ruler) is sinless and infallible, often venerating them and making pilgrimmage to their tombs. Sunnis believe there is no basis for such belief, and that trust, rather than birthright, is the basis for Imam rule. Shiites also look down on some of Muhammad's companions, including his historical successor Abu Bakr, because of their position regarding how leadership was to be passed on. Because of this, Shiites also reject the Hadith (written by the companions), resulting in many differences in doctrine and practice between the Sunnis and Shiites.