There is a glitch that people claim will work to find Mew, but this only works in the original Pokémon games. It does not work in Fire Red.
Any of the Legendaries make for good trade stock. This includes Articuno, Zapdos, Moltres, Raikou, Entei, and Suicune. Also, if you have some of the event Legendaries, such as Lugia and Ho-oh, these will make your trade much easier. Mewtwo will most likely need to be traded in order for your Mew trade to happen. EV-train your trade stock. A group of Pokémon that have been expertly EV-trained will command a much better trade value than freshly-caught Pokémon. Invest some time to build up your team before you start the trade.
There is a chance that you will get a Bad Egg instead of Mew, which will break the game. You will need to load this save file if that occurs. Loading the file will revert the code and rescue your game.
