It saves like every other Pokemon game. You open the menu and select the Save button once ingame.
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If you are using an emulator like VBA to play Pokemon Fire Red then you do not save as you normally do. You save using the emulator controls.
128k, go to emulator>savetype>128k
you go to the top floor in the Pokemon tower and then you save mr.fuji and then he give s u the pokeflute
find the file you designated to hold pokemon fire red files, each save should be numbered, right click and select delete. Done
After you beat your rival will take you to the hall of fame room once your Pokemon are all registered in the hall of fame the game will save itself turn off the game and reopen your file you will end up in pallet town.