Step by step:
Heal your team at the Cerulean City Pokemon Center
Head up Nugget Bridge
Go left until you're right in front of the first patch of grass
Take one step south and immediately press start
Use Abra (or any other Pokemon that knows Teleport) to Teleport back to the Pokemon Center
Defeat the first trainer in the Cerulean Gym
Go back up Nugget Bridge until the menu opens itself
Close the menu and Mew will appear at LV7

Tips:
Mew is hard to catch even in a weakened state so bring lots of Pokeballs. It took me 34 Pokeballs to make this video.