Basic overview:
They believe in Ali RA's right to rule directly after Rasoolullah
's death, due to the events of Ghadir Khum, Rasoolullah
's referring to Ali RA as 'mawla' thus he should be the successor after his
's death....hence the reason they didnt accept the authority of the Rightly Guided Khulafaa. This small faction of people called themselves 'Shiat Ali' (partisans of Ali)...there is also an opinion which suggests that Abdullah ibn Saba underhandedly caused conflicts between the people.
When every Khalifa was ruling, the Shiaa opposed them and thought Ali RA should take over, and after Uthmaan RA's martyrdom, there was even more conflicts between his tribe/relatives (the Umayyads) and the Shiaa....which led to Mu'awiyah's Caliphate after Ali RA's death. There was also the Battles of the Camel and Siffin in that time. However, seeing as the Shiaa gave utmost importance to the blood lineage of the Ahlul Bayt, they didnt agree with this either and pushed for Hassan and Hussain RA to take it. ....and Hassan RA refused and i think he accepted a monetary sum in return and Hussain RA didnt want to dispute it whilst Mu'awiyah's rule was present. But when Mu'awiyah RA died, before Hussain RA could do anything Yazeed ibn Mu'awiyah took the caliphate for himself. This angered the Shiaat Ali even more, because it was seen as a direct offence against the Ahlul Bayt's right to rule....and these people plotted a lot and persuaded Hussain RA that Yazeed would like to meet him and such things and from the time of Ali RA, the capital had been in Kufa...so they pushed for Hussain RA to meet Yazeed.
However, they wanted to cause trouble and Yazeed was told that Hussain RA had set off with an army to attack him...prompting him to send out an army too. They met each other at Karbala where fighting ensued, but Hussain RA's side was not equipped or great in number and they died...only few survived, like his young son, Ali and from him the Ahlul Bayt line continued. All those of the Shiaat Ali seperated themselves off from the Ummayyads and that was the split.
Basically, for Shiaas they believed the ruler should always be a descendent of Rasoolullah
and be male, and this was their 'imaam' who possessed the knowledge close to Allah, he was infallible, free from error and sin...Ali RA was seen as the first Imaam and then after that his sons, grandsons and so on. However, around the 9th century sometime the young boy who was due to be Imaam after his father's death disappeared...he was around 4/5 or maybe slightly older...and it was thought that this was temporary however he was never seen again and then changes were made in rule....where a grand Ayatullah was appointed and this carries on to this day in like Iran...they thought the last Imaam would return again before the End of the World and that he would be Imaam Mahdi...that is the belief of the largest group of Shiites, the IthnaAshariyyah, Twelvers....the Fivers, known as Zaidis hold the opinion that the line continued until the fifth Imaam, they do not place as much glorification of the Imaams as the Twelvers and Seveners (Ismailis, 7 imaams)...hence their closeness in belief to mainstream Sunnis...they are the ones who are seen as 'normal'.
But the others believe in weird things such as:
- The Caliphs collated the Qur'aan and they removed passages which related to Ali RA and same for ahadeeth collections.
- They have their own Shariah Law/tafseer interpretations
- Taqiyyah, concealment of beliefs in certain situations.
- Karbala/Ashura commemoration, feeling the pain and beating themselves with 'every land is Karbala and every day is Ashura. They feel they should take the pain which Hussain RA and his people went through on that day.
- Different Shahada which adds Ali RA's name into it
- Different adhaan/wudhu
- Different salaah, sometimes in method. Mainly with stone from Karbala as headrest in sujood. Combination of salaah so they end up praying 3 times only.
- Prevelance of Mut'ah.
- Dislike of the Khulafaa and Aisha RA
They are regarded as out of the fold of Islaam due to the nature of their beliefs, however there is difference in opinion regarding the Zaydis. BUT some have also declared the Twelvers as part of Islaam, such as old fataawa from Al Azhar, but then again Al Azhar was set up by the Shiiaa Fatimid Dynasty and later came under control of Sunnis. Their belief in taqiyya means that although they may say they dont abuse/dislike the Khulafaa/Aisha RA, you never know if they are saying it for real
erm, i cant think of much else at the mo