Short answers, pulled from the story.
The Lebanese Civil War began on the 13th of April 1975 when unidentified gunmen fired on a church in Ain el-Rummaneh killing four people. This attack was followed by retaliatory killings by Phalangists that led to citywide clashes and all-out fighting between militias.
The two main alliances were the Lebanese Front consisting of nationalist Maronites against Palestinian militancy and the Lebanese National Movement which consisted of pro-Palestinian Leftists. Other groups included the Kataeb Regulatory Forces, Tigers Militia, South Lebanon Army, and Hezbollah an Iran-backed Shia Islamist militia.
Syria intervened with twelve thousand regular troops entering Lebanon on the 1st of June 1976 to conduct operations against Palestinian and leftist militias. Syrian President Hafez al-Assad brokered a truce on the 22nd of January 1976 while covertly moving troops into Lebanon under the guise of the Palestine Liberation Army.
Lebanese Phalangists allied with the Israeli Defense Force killed civilians in the Shatila refugee camp and Sabra neighborhood on the 18th of September 1982. Soldiers loyal to Phalangist leader Elie Hobeika began slaughtering civilians while Israeli forces blocked exits from the area.
The Taif Agreement marked the beginning of the end for the fighting in 1989 as a committee appointed by the Arab League formulated solutions to the conflict. The Parliament of Lebanon passed an amnesty law in March 1991 that pardoned all political crimes and dissolved armed factions in May 1991 excluding Hezbollah.