Fortunately for all of us, TDAXP has a short, Complete Idiot's-style guide to understand what Sunni and Shia believe. To sum it up: Sunnis are like Congregationalist Baptists who want a Pope (Caliph) while Shiites are like Lutherans who believe their leader has been hiding for about 1,300 years.
Of course within Sunni and Shiite there are differences. These range from unaligned moderate Sunnis in Lebanon who live Western-style lives with Christian neighbors to "Jihad-now!" Wahabbis in Saudi Arabia. The Shia have their own divisions like the Twelvers and Ismailis but these groups differ on who were the rightful leaders in the past.
There are also some smaller groups which fall between the cracks. The Alawites in Syria have communion and a greater emphasis on Jesus (probably influenced by the cultural interaction from the Crusades). Also there is also Sufi Islam which is much more personal and mystical than Sunni or Shia. On the fringe are the Druze who can be considered the Muslim equivalent of Mormonism. This is to name only a few of the other denominations of Islam.