Muslims do not worship a different God. Allah is simply the Arabic word for God. Allah for Muslims is The Greatest and Most Encompassing of the Names of God, it is an Arabic word of rich meaning, denoting the one and only God and ascribing no partners to Him.
Allah is exactly the same word which the Jews, in Hebrew, use for God (eloh), the word which Jesus Christ used in Aramaic when he prayed to God.
God has an identical name in Judaism, Christianity, and Islam; Allah is the same God worshipped by Muslims, Christians and Jews.
Muslims believe that Allah's sovereignty is to be acknowledged in worship and in the pledge to obey His teaching and commandments, conveyed through His messengers and prophets who were sent at various times and in many places throughout history.
The most complete system of worship available to human beings today is the system found in the religion of Islam. The very name 'Islam' means 'submission to the will of God.' It is the religion brought by all of the prophets of God for humankind. Islam was the religion of Adam, Abraham, Moses and Jesus (peace be upon them all). The religion of Islam is the complete acceptance of and obedience to the teachings of God, which He revealed to His last Prophet Muhammad (peace be upon him). One who follows Islam is called a Muslim.
Muslims believe in One, Unique, Incomparable God, who has no son nor partner, and that none has the right to be worshipped but God alone. The final revelation is called the Quran. The Quran was revealed to Prophet Muhammad (peace be upon him) in the year 610. Prophet Muhammad (peace be upon him) was a direct descendant of Prophet Abraham (peace be upon him) through his son Ishmael (peace be upon him).
Muslims respect and revere Jesus (peace be upon Him) as one of the mightiest messengers of God. Neither Muhammad (peace be upon Him) nor Jesus (peace be upon him) came to change the basic doctrine of the belief in One God, brought by earlier prophets, but rather they came to confirm and renew it.
Someone can become a Muslim simply by saying with conviction, "None has the right to be worshipped except God and Muhammad (peace be upon him) is the last Messenger (Prophet) of God." Upon becoming a Muslim one's previous sins are all washed away and they come to Islam like a new born baby. (read The Confession).