on red/blue/yellow

PS: read all the steps before doing this

go up the nugget bridge catch an abra to the left of the nugget bridge(trade one for yellow), but don't challenge the trainer. Then, go to the pokémoncenter in cerulean city
Go back to the grass, inside the grass you should see a pokemon trainer don't battle him
go up until he gets of the screen, get in front of him him, but make sure you don't see him.
go one step down but as soon as you see him press start and let abra do teleport. The trainer should see you but he won't manage to battle you because you would already be gone, you'll be teleported to the pokemon center.
your start button won't work, go to the gym and battle the first trainer (the one in the water), beat him.
get out of the gym and heads toward the trainer you teleported away from
the start menu will pop up along the way, close it.
a lv.7 mew should appear, catch it (duh).
for the other one:
go back to the trainer in the grass and teleport again like before.
instead of going to that swimmer in the gym go up the nugget bridge and battle a trainer with a level 17 slowpoke (don't go stand in front of him or your game will freeze, let him walk up to you).
go back to the trainer in the grass and ,the menu will pop up again close it and mew will appear.

(this works for almost every trainer, here are just the trainers to catch mew, if you do the first steps and challenge an other trainer, other pokémons should appear(even missingno.) these pokémon are always on lv.7 (I've caught a lv.7 gengar this way)

you can also go to a gambler on route 8 and fly away to cerulean city, then go battle the trainer with the slowpoke and then go to lavender town and head back to the gambler, the start menu will appear, close it and a lv.7 mew will appear.