We can chart this through the careers of two men - Vedius Pollio early in Augustus' reign, and Pliny the Younger under Trajan - who both intensely courted emperors with varying degrees of success.

Pollio emerges as a particularly unsympathetic member of the early Augustan elite - a Roman eques who served in an extraordinary capacity as governor of Asia in the very early days of Augustus' supremacy. Like most elite Romans, he understood monumental building as the language of power and self-promotion,and an inscription survives from a Caesareum (temple to Augustus' family) which he dedicated in Beneventum in southern Italy. Temples like this were not unheard of - a good number were built over Augustus' reign, particularly in Gaul and Spain - but it was much more common to dedicate something like an altar, and a temple clearly represented a pretty major attempt to curry favour.

More interesting, though, is the story preserved by Cassius Dio, which shows us some more personal ways that he tried to impress the emperor. It's worth the obligatory disclaimer that anecdotes in Roman historians should not be taken at face value - this one in particular became a moral exemplum for reasons that should, hopefully, soon become obvious. However, they did need to be basically plausible in order to work, and therefore the 'throwaway' circumstantial details can often provide good information as to what was considered possible, or likely, for those around the emperor to do.

I'll let Dio tell the story first, and then jump in with some comments:^(1)

Most of the things [Pollio] did it would be wearisome to relate, but I may mention that he kept in reservoirs huge lampreys that had been trained to eat men, and he was accustomed to throw to them such of his slaves as he desired to put to death. Once, when he was entertaining Augustus, his cup-bearer broke a crystal goblet, and without regard for his guest, Pollio ordered the fellow to be thrown to the lampreys. Hereupon the slave fell on his knees before Augustus and supplicated him, and Augustus at first tried to persuade Pollio not to commit so monstrous a deed. Then, when Pollio paid no heed to him, the emperor said, "Bring all the rest of the drinking vessels which are of like sort or any others of value that you possess, in order that I may use them," and when they were brought, he ordered them to be broken. When Pollio saw this, he was vexed, of course; but since he was no longer angry over the one goblet, considering the great number of the others that were ruined, and, on the other hand, could not punish his slave for what Augustus also had done, he held his peace, though much against his will.

This is the sort of person Pollio was, who died at this time. Among his many bequests to many persons he left to Augustus a good share of his estate together with Pausilypon, the place between Neapolis and Puteoli, with instructions that some public work of great beauty should be erected there. Augustus razed Pollio's house to the ground, on the pretext of preparing for the erection of the other structure, but really with the purpose that Pollio should have no monument in the city; and he built a colonnade, inscribing on it the name, not of Pollio, but of Livia.

The end of the story gives one of the usual ways of trying to win favour for yourself and (especially) your offspring - bequeathing some of your wealth to the emperor. This seems to have been common practice under Augustus and become normalised under his successors - the historian Tacitus records that when an aristocratic woman by the name of Junia died, and left considerable sums of money to various patricians but 'left out' Augustus' successor Tiberius, this was considered a slight but one which the emperor bore 'civilly'.^(2) The Pollio story is interesting because it shows how this could backfire - in pointedly rejecting the spirit of the gift and having the house demolished (to build the Porticus of Livia), Augustus would have lost Pollio and his family far more prestige than they could have gained from making the bequest.

However, it's more significant for the question that Pollio had Augustus over for dinner. This was both a way of impressing him with the show he was able to put on - notice how Pollio eagerly furnishes Augustus with all his impressive cups - and of signposting his personal closeness to the emperor: at a traditional dinner party, there were only nine people, and this was therefore both a means for emperors to dispense a highly limited resource - their own personal time and attention. Many anecdotes in Suetonius' Lives of the Caesars are set at senatorial dinner parties, which demonstrates that this was where emperors were expected to spend a fair proportion of their time - he praises Augustus for regularly calling in on senators, especially on their anniversaries.^(3) From the senator's point of view, a dinner party provided an unparalleled opportunity to impress the emperor, perhaps to lobby him in camera, and to bask in his favour; from the emperor's, it was a way of showing deference to the established elite, rewarding loyal or favoured aristocrats, and providing the quid pro quo of prestige on which public service rested.