Short answers, pulled from the story.
The Second Triumvirate was formally constituted by law on the 27th of November 43 BC. It was established by the lex Titia for a term of five years, renewed in 37 BC for another five years, and expired in 32 BC.
The three members were Mark Antony, Lepidus, and Octavian. Their formal title was triumviri rei publicae constituendae, meaning commissioners for the reconstitution of the republic. Octavian was initially the junior partner.
The triumvirs were granted power to issue legally binding edicts, overrule provincial governors, appoint all magistrates, and punish citizens sine provocatione, without right of appeal. Their authority was recorded on the Capitoline Fasti above that of the ordinary consuls.
The triumvirs issued death lists to eliminate political enemies and raise funds through property auctions. Estimates from ancient sources range from 130 to 300 senators and up to 2,000 equites killed or dispossessed. Cicero was among the most prominent victims, targeted for his speeches against Antony.
At the Battle of Actium on the 2nd of September 31 BC, Octavian's forces under Agrippa defeated Antony and Cleopatra. Antony and Cleopatra escaped through a gap in the line, but most of Antony's fleet returned to port without following. His land forces in Greece surrendered afterward.
The Oxford Classical Dictionary warns that 'First' and 'Second Triumvirate' are modern and misleading terms. The label was unknown during the period itself, first appeared in the late 17th century, and only spread into common use in the 18th century. Recent scholarship has begun to avoid the traditional nomenclature.