Fun fact: Savonarola was never actually formally invested with any sort of political power in Florence. Or rather, he was invested with ambassadorial powers on some occasions, but he never had any official role in government.

While the friar Savonarola had no true institutional role, he had certainly been an enormously influential figure: his fiery sermons had been an important catalyst turning the public mood against the Medici, eventually pushing the citizenry to rally against them. His influential preaching would continue to influence the public mood in Florence until late 1497.

That's not to say Savonarola did not actively advise the Signoria, which was reformed after the flight of the Medici from the city: formerly composed of representatives of the city’s trade guilds (and thus individuals susceptible to corruption by bankers like the Medici) the new council was instead composed of eight notables appointed with an unclear selection process (probably with Savonarola's significant input) while all tax-paying citizens over the age of 29 elected an eighty-man body that acted as a sort of supervisory council to which citizens could appeal decisions (separation of powers was not a well-developed concept in Italian political thought at this point in time, and the governing council acted as an executive, legislature, and supreme court all at the same time).

As for Piero (or Pier) Capponi, he was a small-time businessman and statesman initially very close to Lorenzo de Medici, however after Lorenzo's death he joined the faction against the Medicean hegemony (more out of personal disdain for Lorenzo's son Pietro than anything). But rather than a lackey for Savonarola, it would seem that Piero legitimately had the interests of the Florentine Republic at heart: after he was appointed to the governing council, it was he who drove a hard bargain with King Charles of France to guarantee orderly passage through the city's hinterland (the King of France's passage through Italy to claim the throne of Naples had triggered the crisis which saw Capponi and the florentine aristocracy revolt against the Medici in the first place). Capponi would eventually meet his death leading a military expedition against Pisa, a subject of the Florentine Republic which had taken advantage of the chaos to declare independence.

I actually wrote an answer on Savonarola's rise and fall about a year ago.