Mew was given out at a Nintendo event back in the day. I think to get Mew you need to trade down via the games. It'd be easier if you just transfer your pokemon to FireRed or LeafGreen otherwise you are going to need an old Game Boy and a Game Link Cable.
Actually you cannot transfer Pokemon from Gen 2 to Gen 3 so that would not be possible, you can get Mew in Red/Blue version through an in game glitch that requires no additional equipment it's easier for me to show you a link explaining it then for me to explain http://www.ocf.berkeley.edu/~jdonald/pokemon/mewglitch.html but I can attest that this works as I have done it myself.
From that link, the Mew glitch also works for any pokemon you want to catch. Though, the specific link shows you can get mew just by the default.
From what I've read. There was an event to go to certain places and they trade you a Mew. However it's not possible without using glitches now. Cheat devices are not recommended though. What I used was the Long Range Trainer Event Glitch. I think Mew Glitch is the same thing unless they referring to the Old Man Glitch where Cinnabar Island has surf tiles with no Pokemon battle data in. So game gets the player's name to generate a Pokemon. Here's how I remember doing the Long Range Trainer Event Glitch. Please note something could go wrong and lose your save file. If I remember correctly from what I read: Avoid the trainer with a Slowpoke. Who is located near that guy's house that made the Pokemon Storage System in that game. West of Lavender Town. Avoid the old man facing north to that underground. Have a Pokemon learn Fly. Stand at the entrance to that underground mentioned above and save. Now press down and open menu as fast as you can mid-step. The old man shouldn't see even though he should but menu blocks it. Now use Fly and go to the town with Misty's Gym. The old man will see you just when the Fly animation plays but no battle. I think menu gets disabled during this part of the glitch. Defeat that trainer with the Slowpoke without any other trainer seeing you. Fly back to Lavender Town. Now go back to the area where the old man saw you use Fly. As soon as you enter the area. The menu will mysteriously pop up. Close the menu and a wild Lv7 Mew will appear like a wild Pokemon. Capture it and it's all yours. This is how I remember getting mine. Should be able to find info how to do it on Google also. Also, Pokemon Stadium allows it to be used so I'm sure it's clean from what I remember.