Super-short answer:
http://en.wikipedia.org/wiki/Soteriology#Islam
Introductory online answer:
http://www.al-islam.org/al-serat/defaul ... v-salv.htm
Excerpt:
From the beginning, God created the human soul and inspired it with its evil and piety (91:6-7). Thus man is as prone to evil and destruction as he is to righteousness and good deeds. With this choice, however, go sin and repentance, and forgiveness and guidance. Adam did disobey his Lord, but then he received certain words from his Lord and He turned towards him, for He is truly relenting, compassionate (2: 36). Thus Adam sinned and was guided back to God by God through revelation. Adam was both the first sinner but also the first prophet. Every man and woman thereafter carries in him or herself the same potential. This is not to say that every human being is a prophet, but that the goal of humanity is life with God. Nowhere more powerfully and aesthetically has this ideal been interiorized and presented than in the lives and works of the mystics, the friends (awliya') of God, whom we call Sufis.
It has already been observed that every human individual is born in the state (fitra) of innate faith in God as the one and only creator and sovereign lord of all beings. What then, it must be asked, is the role of the prophets in human history? Their role is twofold, first to remind men of their covenant with God, or bring them back to the state of pure faith. Man, according to the Qur'an, is a forgetful creature. The Qur'an was sent, as were other scriptures, from God as a reminder. Indeed, one of the many names of the Qur'an is al-Dhikr (the remembrance). The second task of the prophets, or to be more precise, the prophet-messengers, is to transmit divine precepts or moral imperatives which are to regulate human conduct. In Islam, this is known as the shari'a, or sacred law.
So in Islam you have the dual path to salvation, first of following the law and second by repenting and seeking forgiveness for failing to follow the law (the methods of Judaism and Christianity) but what is distinct is that man has no inherently "fallen" state for mankind. Instead, man is given the capacity for both good and evil in equal measure. Paradoxically this ideal state for free will is also wedded to the concept of predestination and fate, though knowledge of fate resides with God and not with us, we still make decisions.
So even the meaning of "salvation" is totally different than in e.g. Christianity. We are not doomed to die and then saved, we're presented with right and wrong in equal measure and choose the outcome. Prophets and the Law ("Shariah") provide guidance, but all salvation comes directly from God without intermediaries.
I'm ignoring various schools of mysticism here, but this is the mainstream view. The specificity of repentance and compliance also varies from sect to sect. E.g. Wahhabis take a much grimmer view than the faculty at al-Azhar, who take a different view than Indonesian imams, etc. Plus traditional Sunni/Shia distinctions. This is the tip of a theological iceberg, but most religions are naturally rather focused on the subject.