The following is a guide describing the glitch in the Yellow version of Pokemon that allows you to catch Mew, without using an Action Replay, Gameshark, or other third-party device. If done correctly, this procedure will allow you to encounter a level 7 Mew on the Pepita Bridge.
Steps
Step 1. Defeat your rival on the Pepita Bridge
His first Pokemon will be a Pidgeotto at level 20, so it will be useful to have a Rock or Electric type as your first Pokemon. After this step, you will have to defeat all the trainers on the Pepita Bridge, including the last man who will offer you to join Team Rocket.
Step 2. DO NOT face the trainer hiding in the grass to the left of the bridge, as he is a critical component of glithc
Step 3. Save the game, so you can repeat the steps in case you make a mistake
Step 4. Reach the area where the other trainers are, defeating them all and saving after each battle, until you find the trainer who only has one Slowpoke at level 17
Step 5. DON'T FIGHT IT, shut down the game and pick up where you saved
(This is not part of the glitch, so if you already know which trainer you don't have to face, just avoid it and you won't have to turn off the Game Boy)
Step 6. Find and capture an Abra (try searching the grass just above the Board)
It won't be easy, as the Abras will Teleport away after the first turn and end the battle. They are not easy to find and your only option is to throw a Poke ball in the first round and cross your fingers. Once you have captured an Abra you can proceed to the next step.
Step 7. Walk over the Pepita Bridge and save when you reach the end
Now is the time to approach the coach hiding in the grass, which you avoided earlier.
Step 8. Walk in front of him, far enough away that he cannot see you, but only for one square
Save the game exactly there, as the next step can be difficult.
Step 9. Press the down arrow and the Start button at the same time
You will take a step towards the trainer, but the Start menu will appear instead of the exclamation point above his head. Use Abra's Teleporter to return to the Pokemon Center and walk back to the Nugget Bridge. At this point, you will no longer be able to access the Start menu, but don't worry, because this is part of the glitch.
Step 10. Take on the trainer with the Slowpoke at level 17, making sure to walk him at least one step towards you, or the game will freeze
Step 11. Defeat him and use the Teleporter again to return to the Pokemon Center
Then walk up to Ponte Pepita and the Start menu will open.