You can't catch Mew in FireRed. You can only get it in a Nintendo event or from another trainer who has received a Mew from a Nintendo event.
Mew can be traded from Pokemon Emerald after obtaining the Old Sea Map and travelling to Faraway Island. None of the other Pokemon versions which are able to trade to FireRed have Mew as a possible Pokemon to capture of course you can also use an Action Replay or GameShark which can make Mew available in FireRed, but in-game wise there is only the option of trading.
Generation 3 Mew events are over however for Gen 4 and above you could get 999 Pokemon on My Pokemon Ranch and get your ranch to Level 25 and you will be able to get Mew if you trade a Pokemon Egg for it but you can only transfer it over to Diamond or Pearl for non-Japanese versions of My Pokemon Ranch. My Pokemon Ranch costs 1000 WiiPoints which equals to $10 and you can buy it from the Wii or Wii U's WiiWare section.
i have never found it myself, but on YouTube, directly after fighting mewtwo,a person encountered mew but i don't know how.i think they did some certain movement before fighting mewtwo. i tried it and it didn't work. so i don't think you can.
At faraway island by event or gameshark or a cheat without gameshark.
You can't get mew in firered or leafgreen.
Its not possible to get mew in firered only emerald can via Nintendo event.
You can't catch it on Firered you can only catch it in Emerald
Cerulean cave
Pokemon firered emerald
Nope, you have to trade him.
The Cerulean Cave
sadly,no
can't but you can get one from emerald if you have the old sea chart and catch mew at faraway island.
No, you to migrate it from Pokemon firered/leaf green.
Unfortunately, Mew is not a catchable Pokemon in FireRed. It is impossible to catch it without a Cheating Device. Sorry, The interwebs fooled me, too.
No you caan only send it from firered or leafgreen