The following is a sure fire way to get Mew. Requirements: 1) One LDT(Long Distanced Trainer). A LDT is someone who activates the moment you move into their line of sight. Best one is the guy in the Grass to the left of Nugget bridge or the Gambler west of Lavender Town. Furthermore, LDT?s can be reused multiple times. 2) A Pokemon with Fly or Teleport. Hence you can do this glitch relatively early provided you skip the Youngster with the Slowpoke north of Cerulean and make your way South towards Vermilion so you can catch an Abra(which knows Teleport). 3) A Pokemon that can induce Sleep. Mew is a difficult Pok?mon to catch and therefore the best odds at catching it are when it?s Frozen or Asleep. 4) A Pokemon at level 15 or lower. Mew will spawn at level 7 unless you do the following trick when battling the Slowpoke Trainer. Namely if you lower Slowpoke?s Attack stage with Growl, it indirectly affects the level Mew, or any Pok?mon that appears with this glitch, spawns at. You lower its Attack stage to -6 and Mew will spawn at level 1(theoretically not possible and allows for other magic such as getting a huge level boost wherein depending on the Growth rate(Ex: Slow, Medium Fast, etc.) will determine what level it grows to. If it?s fast enough, a Pokemon whose caught at level 1 can be instantly power leveled to level 100). A good Pok?mon for this glitch is Butterfree. It knows Sleep Powder at level 15 and it?s Physical Attack is weak enough that it won?t KO Level 7 Pokemon if you keep it at a low enough level(like level 15). Finally 5) A Trainer you haven?t battled yet. For this trick to work, you need Trainers you haven?t battled. Otherwise you can?t use it. For this instance of the trick/glitch, our chosen trainer is the Youngster with the Slowpoke.
Anyways, here?s how you do it. Step One: Walk to the end of Nugget Bridge and Save your game. If you screw up, you got a stable save file. Step Two: Walk to a point where you?re just off screen of the LDT. Then when you walk into his line of sight, there will be a chance for you to open the menu before the ! activates on the LDT. Takes some practice but once you get the menu open, Fly or Teleport back to Cerulean city. If you?re teleporting, use Cerulean Pokemon Center before you start so it?s flagged as the last Center visited. Upon Flying/Teleporting away from battle, the menu should be unavailable(that?s expected). Step Three: You?ll then want to walk and battle the Slowpoke Trainer. However, you will want to walk in front of the Trainer so that he has to walk at least one square. This is to satisfy the ! from the LDT part. Otherwise the game soft-locks. Battle the Youngster with the level 17 Slowpoke(with 21 Special) and defeat him as normal). Step Four: Upon defeating him, your menu should be available again. Fly/Teleport back to Cerulean and make sure you have sufficient Pokeballs(remember Mew is a pain) along with your Butterfree or Pokemon you wish to battle Mew with up front. Mew only knows Pound Attack so he shouldn?t cause much trouble. Anyways Step Five: Walk to Nugget Bridge. Menu should open on its own, a sign the glitch is working. Press B to close to initiate a wild encounter with Mew.
This works in Red, Blue AND Yellow and is a special case of the Hexidecimal or Ditto Glitch since Ditto is used to force a specific encounter. If the special value of any given trainer?s Pokemon were known, an encounter with Ditto could be bypassed. Meaning in this case, we know the special of Slowpoke so we don?t need to battle wild Ditto to force an encounter with Mew. If we didn?t know Slowpoke?s Special Stat, we would need a Pok?mon with a Special value of 21 and have Ditto transform into it. Remember, when Ditto transforms, it copies the stats of the opponent. Therefore, you?ll encounter a Pok?mon with the Special value wanted via Ditto, hence the Ditto glitch. Red/Blue have it easier than Yellow as you have to go to Cinnabar Island and the mansion basement to encounter wild Ditto in Yellow while Red/Blue can encounter Ditto east of Fuchsia City. Once you encounter Ditto and it transforms into the Pok?mon with the Special Stat wanted, run from the battle and instantly Fly/Teleport back to Cerulean or wherever your LDT you used is located. Hence if you use the Gambler west of Lavender Town, Fly/Teleport back there. If you?re on Yellow you?ll want Teleport, Dig or Escape Rope since you do not want to encounter another wild Pok?mon after running from Ditto. Otherwise it overwrites the value you worked hard for Ditto to copy. After getting back to Cerulean(or whatever town is closest to your LDT) simply follow the last step or walk towards the area where your LDT is located to fight the Pok?mon you want to catch.
I have a video and a similar explanation in the FAQ Nah is making.