Requirements:
Pokémon with teleport or fly
not to have defeated youngster on route 25 (the one with the lv13 slowpoke)
POKE BALLS FOR CATCHING
and possibly some patience.

start off by going to cerulean and going north to route 24. Go to the north end of the nugget bridge and stand right off the screen to the jr. Trainer ( top left of the water just above the grass) and it is reccomended to save there. Press down and start (enter key) and teleport or fly away and you should go back to cerulean and go north to the nugget bridge and fight the youngster with the slowpoke and MAKE SURE TO HAVE HIM WALK UP TO YOU. If he notices you without walking the game will lock up. Defeat him and fly or teleport back to cerulean and go back to the nugget bridge. Your menu should automatically open up and you should exit it and you will encounter a lv.7 mew! Catch it and have fun owning people when it levels up!

I have done what I think is another way to do this glitch although I don't think I did the same thing.

'tis legit

Second of all, you  should be more descriptive as what we should do.

Thank you for sharing this. I have seen several references to the "mew glitch", but never actually knew what it was. This is really cool.

I know one way, but apperently there are a whole bunch of glitches that allow mew to appear, if you do them all, ) mews in total. A party of mews!

thnx for posting that mew glich btw nice post backround Zelda2

I know this thread is a bit old, but in case original poster or someone else sees this: Does anyone know WHY this glitch works? Does this combination of operations somehow unlock the slot of the Pokedex for Mew in the game's code? Always wondered about these glitches. Saw a video on my the MissingNo. glitch happens too. Pretty cool stuff to investigate.