The method by which city and community representatives were appointed is not clear (royal appointment, direct popular election, or appointment by local authorities).
When the Grand Equestria Pony Summit assembled every few years, they usually petitioned Princess Celestia to settle matters by royal decree. Celestia herself presided over the summit and gave the royal assent to proposals made by summit delegates.
With the return of Princess Luna and the promotion of Princess Celestia and Twilight Sparkle to Alicorn princess status, it can be assumed Celestia will now give one of the other princesses the responsibility to summon the Grand Equestria Pony Summit and grant the royal assent to proposals given by delegates.
Equestria is slowly evolving into a parliamentary representative system, much like the rise of Parliament in relationship to the English kings centuries before the kingdom of England merged into the larger British United Kingdom in 1707.