First, I did my research. I read this page http://www.ocf.berkeley.edu/~jdonald/pokemon/mewglitch.html

Then, when I had read enough to understand how it worked, I beat every trainer on route 24 and 25 except the Youngster with the Slowpoke. Then I played to Vermilion City and caught Abra and Jigglypuff on the route before the city and Drowzee on the route after the City. Went trough Diglett's Cave, traded my Clefairy in for a Mr. Mime, caught a Diglett too. On the route to the right of Diglett's Cave, I noticed a trainer that was off the screen right before he saw me. Instead of facing him, I hatched a brilliant plan.

Perhaps I didn't need Fly if Teleport could get me to Cerulean City before the trainer saw me. I went back to Cerulean City and healed at the centre. Then I took the four minute hike back to the trainer and saved just above where he was able to see me. He saw me before I could hit start the first time, so I exited and rebooted the game and tried again. This time I switched the return key task to my right hand (I'm right handed so it can move quicker) and managed to press return before the trainer saw me. Selecting Pokémon, I used Abra to teleport to Cerulean City. In Cerulean City, I checked to make sure my start button wasn't working. I tapped return and nothing happened. So far, so good.

I approached the Youngster and battled him just as the web page said and then used Teleport again. From Cerulean City, I once again braved the hike while carefully avoiding the grass on the route before Vermilion City. When I stepped onto the route after the city, my menu popped up. Carefully pressing the key designated for the "B" button on my keyboard, I found myself in battle with Mew. He knocked out my Jigglypuff and really gave it to my level 15 Drowzee, but my tough elephant Pokémon pounded him into the red zone and put him to sleep. After that, it just took two Poke balls to catch him.

That is the story of how I caught a Mew for the first time ever. I wish everyone the same success. There is also a bug catcher on the route before Vermilion. If you want to catch a Mew even sooner, go left towards his patch of grass and Teleport to Cerulean City to start the glitch.
Also, save before dangling the trainer and after catching Mew only, as doing so in between will disrupt the glitch.

Ah, I love the Mew glitch. It's fun because it's challenging to do, and you get nicely rewarded in the end. Too bad you can't bring that Mew to the 3rd gen and up games.

I wonder how the first person discovered this glitch. It looks way too complicated to be done on accident.

I am almost sure that someone from Nintendo had to have leaked this glitch. The glitch is just too convoluted to be just found by accident. Who ever found it I congratulate them because I can barley do it with instructions.

billythekidmonster : Well, the only thing we know for sure is, that gamefaqs.com found out about it and told everybody 8 years ago and soon everyone had a page that describes how it is done. Like me! I'm one of those people now. I chose a story format for this page so maybe I'm one of the special ones who don't get off on telling people the precise way to do things. I just find it so annoying when someone tells me directly how to do something down to the last detail which I already know about.

So to summarize, "mommy issues". I'm going to go cry into my X-men comic now.