How do you catch Mew in Pokemon Blue?
You can easily catch a Mew right at the beginning of the game,
after fighting misty and a bit before going to bill's house. Use
cerulean's pokecenter to heal your Pokemon. THIS IS VITAL. Then, go
and catch an Abra. DO NOT FIGHT THE MAN IN THE GRASS TO THE LEFT OF
THE TOP OF NUGGET BRIDGE. IF YOU DO, THE GLITCH IS RUINED. You must
not have fought either this man or the youngster facing north with
a slowpoke near bill. After catching an Abra, put it in your party.
Save the game, and walk to the top of nugget bridge. Walk to the
corner of the water directly to the left of nugget bridge, closest
to the man. Save the game. Now, press down and hold start
immediately afterwards. Release it when the menu comes up. Tell
Abra to teleport. When you've done this, and done it correctly, the
man will see you as you teleport away. Upon landing, your start
button will not work. Walk up nugget bridge and fight the youngster
with a slowpoke. You must let him walk to you, or the game will
freeze. After you beat him, your start button will work again.
Teleport again and walk up nugget bridge after landing. About 1/3
of the way up, your menu will come up by itself. If you press the B
button, the menu will close and a battle will begin. A level 7 mew
will appear, and it is hard to catch. Using a low level (7-9)
Pokemon to get its HP down and then putting it to seep with a
jigglypuff will allow it to be caught easily with a pokeball.