How did Roman emperor Tiberius become a Roman emperor?

Tiberius was at first least likely to succeed Augustus. Augustus' designated heirs was at first Marcellus, his nephew and his daughter's husband. When he died in 23 BC, Augustus married his daughter Julia to his close friend and right hand, Marcus Vipsanius Agrippa. They had 5 children of whom 3 were males. These were Gaius, Lucius and Postumus. Gaius and Lucius, became the designated heirs. Gaius and Lucius died.

The death of Gaius in AD 4 initiated a flurry of activity in the household of Augustus. Tiberius was adopted as full son and heir. In turn, Tiberius was required to adopt his nephew, Germanicus, the son of his brother Drusus and Augustus' niece Antonia Minor. Along with his adoption, Tiberius received tribunician power as well as a share of Augustus's maius imperium, something that even Marcus Agrippa may never have had. Thus, when in AD 13, the powers held by Tiberius were made equal, rather than second, to Augustus's own powers, he was for all intents and purposes a co ruler with Augustus, and in the event of the latter's passing, would simply continue to rule without an interrernim or possible upheaval.

Augustus died in AD 14, at the age of seventy-six. He was buried with all due ceremony and, as had been arranged beforehand, defied, his will read, and Tiberius confirmed as his sole surviving heir.