A fast way to earn how much gil?
A fast way to earn a quick buck is to farm Quadav Helms from Old Quadav in Beadeaux. Just turn them into the Galka in Bastok Mines for 900 gil each. It's fast money because you don't have to sell anything on the AH.
The fastest way to earn any amount of gil would be to get lucky gambling... or Mog Bonanza... instant millions if you get lucky.
Please be more specific in future questions.