Born in Rome on October 24, AD 51, Titus Flavius Domitianus was the youngest son of Vespasian and Domitilla. He was raised in an era of great family mobility, as Vespasian gained several key appointments under both Claudius and Nero. However, despite these appointments (ie the proconsulship of Africa), Vespasian was under considerable financial hardship (for a man of his position). Though Vespasian was forced into several undesirable financial moves, such as mortgaging his property to his brother, he never lost his seat in the Senate (which required stringent levels of financial means) and reports of Domitian's youth in poverty are quite exaggerated.
Domitian was left in relative isolation from his primary family. Vespasian and oldest son Titus spent much of Domitian's youth abroad in various services to the empire, while Domitian's mother had died at a relatively young age. Though the details of Domitian's youth are largely unknown, it is definite that his education was on par with other Senatorial elite of the time and that the future emperor excelled in such courses as rhetoric, literature and poetry. He was also praised for his skills in oratory, a skill that would surely aid him in his future political endeavors. It is during this time that Domitian supposedly developed a preference for solitude (largely from Suetonius), but this does not necessarily conform to his later career. While he would certainly show issues in relating to members of the Senate and the imperial court, his difficulties seem more to be matters of tyrannical control than withdrawal.
Regardless, Domitian's life, like those of many Romans, took a tremendous shift with the suicide of Nero in AD 68. As civil war raged, with Galba, Otho, Vitellius and others vying to fill the power vacuum, Vespasian began to conspire while suppressing the revolt in Judaea. When Vespasian eventually declared his intentions to grab power for himself in the summer of AD 69, with the support of Syrian governor Gaius Licinius Mucianus, Domitian remained in Rome, likely in the home of his uncle Titus Flavius Sabinus the city prefect. Despite the odd circumstances Sabinus remained in his position throughout Vitellius' rather short reign in Rome and Domitian seems to have been free of any backlash associated with his father's rebellion. Vitellius understandably though, certainly had more pressing matters to attend to, such as Mucianus marching on Rome with 20,000 men from the east, and an uprising of the Danubian legions in favor of Vespasian.
Much to the disappointment of Mucianus, the revolting German legions under Antonius Primus stole the glory and defeated the Vitellian forces at Cremona, paving the way for Vespasian to claim victory. While this was good news to the Flavian cause, it left Rome in a state of panic and turmoil. As Primus continued to march, Vitellius with only the Praetorians between him and the now victorious Flavians, knew his time as emperor was short. Mucianus offered him a deal, in which Domitian's uncle Sabinus acted as mediator, offering Vitellius safe passage if he would simply abdicate in favor of Vespasian. Vitellius agreed, but the Praetorians and other Vitellian supporters were angry (and assuredly fearful of the coming Danubian forces). Sabinus, as the local face of the impending change, was confronted with the brunt of this anger and was killed in the riots that followed. Domitian meanwhile was certainly also in a precarious situation. The exact details of his escape from the Vitellians is in doubt but both Tacitus and Suetonius have him rescued in some capacity by members of the cult of Isis, where he likely remained in hiding until the arrival of his fathers forces.
Shortly thereafter (December of AD 69) Primus arrived and began to turn the tables on the Vitellians with his German Legions. Vitellius was dragged from hiding and butchered while invaders were given a free reign of terror over the city. Fortunately, Mucianus arrived just a few days later and set about restoring order, but it was obviously too late for Sabinus. Domitian however was given a grand opportunity to become a major player on the world's biggest political stage. He presented himself to his fathers supporters and was immediately hailed as Caesar. Acting as the front man (Mucianus certainly held equal authority as Vespasian's primary advisor) for the new regime, Domitian ably administered the Flavian administration. Eager to match his brother and father's military glory, Domitian soon marched to Germania to put down a revolt of the Batavian auxilia, but it died out before anything of note could be accomplished. Shortly thereafter, Domitian was married to Domitia Longina, the daughter of the great general Gnaeus Domitius Corbulo, who was forced to commit suicide under Nero. Securing the support of the anti-Neronian camp through his son's marriage (not that he likely needed to, but this arrangement certainly helped to cement any alliance), Vespasian soon returned to Rome, and Domitian was relegated to relative obscurity.
It was suggested that Domitian dedicated himself to further studies in the arts while Titus gained military glory in Judaea before returning to Rome as a hero primary heir to Vespasian. However, while Domitian clearly took a secondary role to that of Titus, he did serve as Consul 6 times during his father's reign and was not completely removed from imperial politics. After Titus took over from Vespasian in AD 79, there is some speculation that the brothers maintained an unhealthy relationship, but there is really nothing other than rumor and innuendo to support this. Regardless, there is little mention of Domitian's activities in government or elsewhere during the reign of Titus, but he clearly was marked as 'Caesar' or heir (as Titus did not have sons of his own). When Titus died possibly of a brain tumor just two years later (and not without the appropriate level of insinuation that Domitian gave him poison) Domitian eagerly went to the Praetorians and had himself declared the next emperor. Among his first acts was to support his brothers deification and to finish the triumphal arch honoring Titus' victory in Judaea.