How and why did the so-called First Triumvirate come into being? How successfully was it opposed?
This was an unofficial and originally secret political partnership. At the time it was not known as a triumvirate, as this is a modern term. At the time it would have been known as an amicitia - to supporters or factio, meaning a gang of three, to the enemies. The three triumvirs were prominent individuals, they had great resources: Crassus had money, Pompey had influence, respect and now more money than Crassus, and Caesar had diplomatic skills along with the consulship in 59. We are not sure precisely when it was formed, but we know it was between summer of 60 and spring of 59.
The partnership was underscored by a marriage between Pompey (recently divorced from Mucia - ½ sister of the Metelii), and Julia, the only daughter of Julius Caesar who was about 17. Caesar recently divorced from Pompeia after the Bona Dea scandal, married Calpurnia who survived him and was the daughter of L. Calpurnius Piso - Caesars candidate for the consulship of 58.
It has come into existence because the three members had each been obstructed by the extreme optimates under the leadership of Cato. Their requests were no means outrageous, but the optimates seemed to have been very short sighted and without realising it they were driven into each others arms. Crassus wanted to make a contract with then Asian tax collectors as he had financial interests at stake. Cicero supported this as it would help relations between the knights and the senate, which he thought was fundamentally important, but the proposal was rejected. Pompey wished for land to be provided for his veterans and to have the eastern settlement ratified in one go, instead of every one of his actions be debated. Caesar wished to gain a large pro-consular command instead of being in charge of forests in some insignificant part of the empire, which was the optimates plan.
When Caesar was in office in 59, the first thing he did was providing land for the veterans, and he constructed the agrarian bill, which would distribute land to the poor as well as the veterans. The senate rejected the idea, so Caesar brought the bill to the people who accepted it. Caesar, with the help of his tribune Vatinius carried the bill to ratify Pompeys actions on block. He then was successful in paying Caesars debt to Crassus by a measure, which remitted one-third of their contract to the Asian tax- collectors. Vatinius then proposed that Caesar receive an extra-ordinary command in Cisalpine Gaul and Illyrcium for five years with three legions and the right to appoint his own legates and to found colonies. On top of this he received Transalpine Gaul and some support from Germany from Ariovistus a German chieftain
In 59 the triumvirs prevailed in the political struggle against the optimates. P. Vatinius, loyal Caesarean, in office as tribune and Pompeian veterans to influence how the electorate voted. In 58, it was the same - both consuls sympathetic, Piso to Caesar, Gabinius to Pompey. Publius Clodius was tribune (financed by Crassus) but he was not as reliable as Vatinius. The urban plebs were passionately supportive of Clodius because he had introduced free food for the poor. So up until this point they were entirely successful and the objectives of the formation of the triumvirate were all seen to and equally importantly it was proof that the triumvirs were able to defeat the optimates in their measures. Cato also was arranged to be removed - to supervise the annexation of Cyprus, which he accepted from early 58 to 56 - He did it because it was a good opportunity for him financially - but also they went because they were afraid that their opposition would lead to civil war.
Once Caesar had left Rome there were problems, as Clodius began a series of humiliating attacks upon Pompey, by street gangs and so Pompey stayed in his house for a few months until Milo created a gang which supported Pompey and so Pompey was safer, but this is evidence that at the time the political tension must have been very obvious and that the streets of Rome must have been increasingly more violent thought the years.
To sum up, the triumvirs managed to achieve all their objectives and therefore in that sense they were totally successful and the opposition was totally destroyed, as Cicero was exiled and Cato was sent abroad, and on his return he was successfully prosecuted for extortion.