There were a multitude of things about Augustus that made him so successful, I'll cover a few. First off he was surrounded by an intelligent council who were not afraid to speak their mind. There was Marcus Agrippa and Gaius Maecenas.

Military: Augustus' military and architectural advisor Agrippa was a huge reason for his success. Now Marcus Agrippa was Augustus' extremly close friend since an early age because of Augustus' pleading of his uncle (Ceasar) to spare Marcus' older brother Lucius Agrippa for fighting against Ceasar under Cato the Elder in North Africa. From then on Agrippa was unquestionably loyal to the young emperor. His military succes is most notable in the battle of Actium that pretty much hoisted Augustus in to the emperor postion. His importance cannot be overstated, without Agrippa Augustus wouldn't of been able to win his wars.

Political: Gaius Maecenas was the flip of Agrippa, a savy politician Maecenas was useful in the propaganda war against Antony. He was maybe not as important as Agrippa but still very usefull as he acted deputy for administrative purposes while Agustus was away on war and other buisness.

How Augustus got into power was impressive but not all that special, as you see the countless other times in Inperial roman history, conquest. What differntiated him from the rest was how he controlled his power. What so many emperors of rome faile to see was that naming yourself outwright ruler or demeaning the senate was often a recipe for death, think Ceasar or Nero's absolute hatred for the cenate. Augustus realised that if he stayed behind the scenes a bit more and gave the senate their autocracy, that no one would really mind. Also his public works projects made him popular with the people.

Lastly, one should understand that the empire was tired after 2 civil wars with little downtime between them, the people who may of had a problem with Augustus liked the pax romana more than a few tax increases or adultery laws.

Edit: Spacing

Teizke makes some great points and to build off of his post, Augustus had the luxury of being much younger than Caesar when he took power. Caesar tried to shoehorn his policies and reforms quickly because he thought he had little time to enact his reforms. He was not just older than Augustus but he had spent many years before his reign at war in Gaul and then with Pompey so the stress may have gotten to him. Augustus on the other hand was younger. He would have taken a less personal role than Caesar in the battles during the civil war. He had the luxury of having more time to enact his policies which allowed him to be more subtle in his approach to governance. Instead of making himself dictator he became the Princip or the first citizen of Rome which gave him an elevated status but didn't use the terms of monarchy that had built up such a stigma which minimized popular backlash.