Rushdie fully expects the reader to suspend belief right from the last line of the first paragraph:
Just before dawn one winter's morning, New Year's Day, or thereabouts, two real, full-grown, living men fell from a great height, twenty-nine thousand and two feet, towards the English Channel, without benefit of parachutes or wings, out of a clear sky. (p 3)
Gibreel Farishta and Saladin Chamcha are the miraculous sole survivors of an act of terrorism and wash up on the beach of England. Each begins to display characteristics representative of an otherworldly being - one displays a halo, the other a pair of horns - setting off a story of acceptance and forgiveness interspersed with commentary on tolerance, faith/doubt, megalomania, and identity. Gibreel and Saladin form the frame narrative as we learn each man's history and as they try to piece their lives back together in the wonderfully titled section "Ellowen Deeowen". Gibreel (as the incarnation of the archangel Gibreel) develops visions of the prophet Mahound at the time of his revelations in Jalilia (an interpretation of the life of Muhammed in Mecca) as well as those of a modern Indian peasant girl, Ayesha, who moves an entire village to walk to Mecca - through the Arabian Sea - based on the belief in her revelations from the archangel.
There are many character and narrative threads in The Satanic Verses and they don't all start to come together until late in the novel. This is a novel to be savored and pondered with wonderfully evocative imagery. There are also many "doubles" in this novel - two Hinds, two Mishals, two or three Ayeshas (depending on how you count), Gibreel himself and Gibreel the archangel, and a Salman (who might mirror the author depending on how you look at it) - so you must also read The Satanic Verses closely.
This is a controversial novel, there is no getting around that. When the prophet Mahound issues a proclamation from the archangel that women are to be sequestered, a madam comes up with the idea to have her twelve girls take on the personalities of Mahound's twelve wives; the brothel receives a boost in business from the scheme but the brothel is eventually shut down and the prostitutes and collaborators are executed. Because the novel uses the life of Muhammed as a basis, the idea that prostitutes are imitating the Prophet's wives can be offensive to some. Do you want to know what I think? Those people don't have to read The Satanic Verses, same as people who don't like to see novels about the life of Jesus Christ that depict him doing un-Christlike things don't have to read those. A novel isn't real, just like any historical novel using the Tudors as basis isn't any more real just because it uses King Henry VIII as a main character. Some events will be made up for storytelling purposes. No one is forcing you to read it.
The novel also brings the issue of faith and doubt to the fore with the visions of Mahound and Ayesha the peasant. How is someone believable when he or she claims to be the mouth of the archangel and brings revelations from God? What do you do when the prophet suddenly retracts a previous statement, claiming it came from an "evil" source? This is the controversy over the so-called Satanic Verses, a sura attributed to Muhammed that affirmed prayer to three old female polytheistic deities from the regions around Mecca but later retracted as the work of Shaitan (the devil). Since the archangel only reveals information to a prophet, never to anyone else, how do we know if the revealments are the actual Will of God? It requires faith, same as the village that follows Ayesha the peasant on a pilgrimage to Mecca, on foot, through the Arabian Sea; Ayesha affirms that the sea will part for them and the faithful will walk across the seabed; there are believers and there are doubters. Like Doubting Thomas of the New Testament, does one need proof of the Divine to make the leap of faith?
The Satanic Verses is much more than just a book that pushes buttons for the sake of pushing buttons. If those buttons set you off, then perhaps you ought not to read this book. If you do read, look beyond those hot-buttons for the journey of Gibreel and Saladin; it's a crazy ride and, ultimately, a very satisfying one.