This is what happened before Vespasian came along: Caesar Augustus ruled long and effectively leaving his adopted son Tiberius to take over. Tiberius did well at first, but then lapsed into depression and went on an extended, x-rated vacation in Capri -- operation of the Empire fell into the hands of his unscrupulous cronies. Tiberius died of natural causes after making vague arrangements for his nephew Caligula to succeed him. Caligula turned out to be insane although some modern historical revisionists say his reputation was posthumously much sensationalized. But, luckily, his reign of terror lasted only four years until the Praetorian Guard killed him and then chose his uncle Claudius to be next. Claudius was also mentally unstable and was married to the even nuttier Messalina. Together they had hundreds of officials executed before Messalina's sexual excesses caused her own downfall. Claudius's next wife, Agrippina Minor, spent most of her time ensuring that her son by a previous marriage (Nero) would succeed Claudius, but she did end the Senatorial killings inspire by Messalina. Claudius died of acute alcohol poisoning, and Agrippina's son, Nero, got the throne, as she had planned. Nero was the last and nuttiest of the Julio-Claudian bunch, and, after the disastrous fire, after the excessive spending on his Domus Aurea, and after the provincial armies rose in revolt, he committed suicide -- one step ahead of the arrival of the Praetorians and the mob, who gladly would have done the job if he hadn't. Nero's death in 68 AD was followed by the "year of the four emperors" as Galba, Otho, and Vitellius came and went, and, finally(!), Vespasian himself came to power.
Vespasian sprung from the equestrian or knightly class, not the nobility. He was the son of a tax collector in Rete (Modern Riete) a town north of Rome. The only members of his family that had held public office before him were a maternal uncle in the Senate, and an elder brother who had been a military commander, Senator, and Prefect in Rome. Vespasian followed in his brother's footsteps and eventually surpassed him, holding military commands and getting political appointments from Caligula and Claudius. He was passed over in the early years Nero's rule, but finally was given a job as Proconsul (governor) in North Africa. There he first got his reputation as a penny-pincher, which really meant that he kept his accounts honestly and rigorously and did not allow the profligate spending which was ruining the rest of the Empire under Nero.
In the fall 66 AD he went with Nero's entourage to Greece -- Nero wanted to perform in the famous Greek theaters -- and, according to legend, Vespasian fell asleep during one of Nero's poetry readings. In February he was sent off with a special command to put down the Jewish rebellion in Judaea. Some historians say he was given the command in spite of dozing off while Nero was on stage, but others say Nero wanted to humiliate him by giving him an impossible mission: two previous commanders had failed. Nero could, at any rate, feel safe with Vespasian in Judaea: if Vespasian failed, it would be the end of him, and if he succeeded, his humble origins would keep him from trying to displace Nero. The sequel was, of course, that Vespasian somehow acquired three legions and a large additional force of mercenaries and did a job on the rebellious Judaeans in two successful campaigning seasons (spring 67 and spring 68).
When Nero killed himself in 68, Vespasian stopped fighting outside Jerusalem. He sent his elder son Titus to negotiate with the rival Roman Governors in Damascus and Alexandria, and then the eastern provinces waited while Nero's would-be successors fought it out. Galba was killed by Otho (January, 69 AD), and Otho became Emperor. Then Otho and Vitellius fought each other for control. Otho lost and committed suicide (April, 69), and forces loyal to Vitellius took over Rome and proclaimed him Emperor. On July 1 the eastern governors made their move. The legions in Egypt proclaimed Vespasian Emperor followed within days by the legions in Judaea and Syria. The rest of the provincial legions agreed by mid-month, and the Danube "frontier legions" followed in August, leaving Vitellius with only the home legions in Rome. One Danube commander loyal to Vespasian made an unauthorized charge down the Italian peninsula and finally took Rome, but not before Vespasian's brother was killed by the Vitellians in a battle for the Capitoline Hill. On December 20, 69 AD Rome fell to forces loyal to Vespasian (who had himself not yet left the East), and Vitellius was murdered by his own troops. The Senate acclaimed Vespasian the next day, and he was later granted specific powers by law, a new procedure which had not been followed by the previous emperors. He finally returned to Rome in October of 70 AD, after his forces had mopped up remaining Vitellian resistance on the peninsula. Vespasian himself always dated his rule from July 1 of 69 AD, the day on which the Egyptian legions had named him Emperor, rather than the date that the Senate had taken its actions or the date of his return to Rome.
Vespasian had three things to do to consolidate his power. First, he set about restoring the state's fiscal position, which had been almost destroyed since the death of Augustus and especially by Nero's excesses. He announced that state revenues had to be tripled and immediately instituted new taxes, abolished old tax exemptions, and evicted squatters from state lands (the same things he had earlier done in Africa and the east.) Exactly how much new revenue he collected is unknown, but it was enough: he did restore confidence in the currency and accumulated a budget surplus. Although some of these measures were resented by the people who paid, most Romans were mollified by his large building programs (including a new Forum and the Colosseum) and by generous distributions of state and personal wealth to needy friends, to the military, and to the Roman public. His fiscal programs were undoubtedly helped by the fact that he was personally incorruptible -- although he was accused of greed, it was always for the benefit of the state.
Vespasian's second task was to stabilize the military situation. He brought the Praetorian Guard back to its normal size, reversing the expansions put in place by Vitellius, and regrouped the frontier forces by moving out officers suspected of Vitellian loyalties and sending two more legions to the east. His son Titus finished the war against the Jews with the capture of Jerusalem in August of 70 AD and a cousin put down a revolt in the Rhineland. Some borders were rationalized and new border commanders were appointed. But the most important change was that Vespasian was the first emperor since Tiberius to have any real military experience -- as commanders-in-chief Caligula, Claudius, and Nero had all made ridiculous military decisions that had led tow their own downfalls and set up the civil wars that followed Nero's suicide. Vespasian reintroduced military discipline. Ironically, Vespasian's own son Titus was the greatest threat to military stability: after taking Jerusalem, his troops had wanted to march with him to Rome. Instead, Titus came back alone and loyally submitted to Vespasian, and, instead of asking for a personal "triumph", he celebrated a joint triumph with Vespasian. Vespasian thereafter treated Titus almost as a co-emperor, and he made it quite clear that the immensely popular Titus would be the next Emperor. (Vespasian's other son, Domitian, was very unpopular. During the battles against the Vitellians, Domitian had virtually run amuck in Rome. He was kept on a very short leash throughout the reigns of Vespasian and Titus.)
Restoring public respect and adulation of the office of the Emperor was Vespasian's third task, and he was, obviously, well placed to do this. He had several things going for him, not least of which was that he was neither a raving Julio-Claudian nor an inept pretender like Galba, Otho, Vitellius (and several others who tried to be emperor in the year before Vespasian came to power). One of Vespasian's first moves was to tear down most of Nero's vast and expensive private estate, the Domus Aurea, and replace it with facilities available to the pubic. The most important of these was undoubtedly the Colosseum, which he built on the site of the duck pond in the courtyard of Nero's Domus -- yes, it was a huge courtyard! (What now is called the Domus Aurea was only a small dining pavilion on the back side of Nero's estate, and it only survived because Vespasian filled it in to serve as foundations for other things rather than just knocking it down.) Vespasian built housing in some areas reclaimed from Nero's estate, and his big public building projects -- his forum, the Colosseum, and the Baths of Titus -- meant that more money was going into capital investment, and into the pockets of contractors and workers, rather than being wasted on Julio-Claudian excesses or civil wars.
Vespasian was solidly successful in all three of his tasks during his own lifetime, and he passed on a fiscally sound state, a loyal, strong, and agile military, and, most importantly, a popular government to Titus. He had essentially reversed the rapid downward slide of Rome that had begun with the depression of Tiberius. Also, and most importantly, he had ensured that Titus got all the training and experience that he needed to run the store when he took over on the death of Vespasian in June of 79 AD. The only thing that could really upset the plan was what, in fact, happened.
Titus died only 26 months after Vespasian, and the crown passed to Domitian, Vespasian's mentally disturbed second son, who had run riot during the battle for Rome. There is no evidence to support stories that Domitian somehow hastened the death of Titus. Domitian ruled from 81 to 96 AD and turned out as bad as the worst of the Julio Claudians. Some modern psychologists say he suffered from post-traumatic schizophrenia, the result of a historically verified head injury. The Flavian dynasty that started with Vespasian did manage to eventually straighten itself out. Nerva succeeded Domitian and began the era of the "five good Emperors" -- Nerva, Trajan, Hadrian, Antoninus Pius, and Marcus Aurelius -- that lasted until 180 AD..
There are many good sites on Vespasian on the Internet. Among the best are:
A biography from DIR (De Imperitoribus Romanis, meaning About the Roman Emperors): http://www.roman-emperors.org/vespasia.htm
A biography from Britannica.com: http://www.britannica.com/bcom/eb/article/3/0,5716,77153+1+75174,00.html
A Britannica article on the Flavians (part of an excellent historical survey of Roman History): http://www.britannica.com/eb/article?eu=77153&tocid=0&query=vespasian&ct=
Complete texts of the two best ancient sources, Suetonius and Tacitus, are both on the Internet. Tacitus is available in English and Latin, but Suetonius is only available in Latin (any volunteer translators?):
Tacitus -- Histories -- five gossip laden "books", really chapters on Vespasian, Titus, and Domitian (written in 109 AD): http://classics.mit.edu/Tacitus/histories.html
Suetonius -- "Life of Diefied Vespasian" from The Twelve Caesars (Julius Caesar through Domitian). Straighter history -- much less gossip. It is in this biography that Suetonius described Vespasian as always looking as if he was trying to relieve his constipation: http://www.gmu.edu/departments/fld/CLASSICS/suet.vesp.html
The Humor of Vespasian: http://www.cstone.net/~jburns/gasvesp.html