Ok so you need just have beaten the 2nd Gym Go out of Cerulean City and catch an Abra. Once you catch one, save your game (Optional) then head back to Cerulean City, then go up nugget bridge then turn Left, then there is a trainer (He must be battle-able for this to work) make sure you're in the same lane he is. Then save (Recommended) Then go down, hen he begins battling start up your game again and REMEMBER the exact stop you were when he walked up to you. When your one step away, take that one step but as soon as you do press start. Your menu will appear. Choose Pokèmon, Abra, Teleport and you should Teleport back to Cerulean City PokèCenter. Then if done right, your start button wont work. Head back up nugget bridge and What the? Did you just press start or did it pop up. Then exit out of the menu and a battle will begin. Who is it? It's Mew Lv 5 .

Mew can be captured with an ordinary Pokèball, Try Paralyzing Him with Thunder Wave then just try lower his health. He's Pretty easy to catch.

This Glitch/Easter Egg can also work in Red or Blue Version. It doesn't work in FireRed, LeafGreen, HeartGold, SoulSilver.

If Mew is caught then the game is pretty easy to Complete mew can learn any Move possible, Grows levels easy enough. So what more could you want?.

Extra Info: You can catch Mew a Second time at Cinnabar Island, by reading all the diarys in the building in Exact order. Then you can find Mew again(Or first time)