Below are the methods on acquiring Mew in the Generation I Game Boy Games.
To acquire Mew at the earliest point possible in the game, the player must not have defeated the Swimmer in Cerulean Gym and the Junior Trainer (the one who says "I saw your feet from the grass" when the battle with him begins) on Route 24 (West of Nugget Bridge) in the grass. It is prudent to save before doing this. The player must defeat Nugget Bridge as usual without engaging a battle with the Junior Trainer.
Before attempting this glitch, it is ideal to have several Poké Balls stocked up. Note that the player must have an Abra that can teleport, and therefore cannot be playing Yellow version unless he or she has reached Route 5 or traded for one prior to attempting the glitch.
The player then needs to return to Route 24 and catch (or trade over) an Abra, or withdraw the Abra if it is in the PC, then return to Route 24 if not already there. The player then needs to stand above the Junior Trainer so that he is just offscreen. Then the player needs to move down until seen, and immediately press START. The player then needs to use Teleport with Abra. If done correctly, the trainer should get the indicative exclamation mark while the player teleports. At this point, the Start menu will not work until you battle someone though it is imperative to not battle anything or anyone else or talk to anyone (including the Youngster with the level 17 Slowpoke on Route 25 if the player wishes to use the alternate method, see below).
The player then needs to head east from the Pokémon Centre into the Cerulean City Gym and battle the Swimmer. After defeating the Swimmer (the Start menu should be available upon defeating him), the player then must head to Nugget Bridge and after several steps the Start Menu appears. Upon closing of the menu, it should begin a battle with a Lv. 7 Mew.
Note: This method, if executed correctly, will always result in a wild Mew regarldess of the last seen Pokémon's Special stat.
Method #1 (Alternate method)
The player must follow the steps for Method #1 exactly until they teleport from the Junior Trainer using Abra. Again, the Start menu will not work after teleporting. The player then needs to head north towards Route 25 and battle the Youngster. As in Method #1, it is imperative to not battle anything or anyone else or talk to anyone before then. The player must engage in battle by him seeing them (and must walk against the wall to be seen, not towards him or the game will freeze).
After defeating the Youngster, the player then needs to walk towards Cerulean City. After a small amount of steps, the Start menu appears. Closing it should begin a battle against a Lv. 7 Mew.
If used on other trainers other than the Youngster, it will often be a different Pokémon (depending on the trainer's Pokémon's Special stat); for instance, doing so with the Lass below the Youngster will result in finding a Lapras, which is normally only available at Silph Co.
For this method, the player needs to go to the Gambler in front of the Underground Tunnel entrance east of Saffron City, and stand above him so that he is just off screen. The player then needs to take one step down closer to him, but make sure that he does not see the player, and then immediately press START. If the player is spotted, the glitch would fail. If it was successful, the menu will appear and the player will be able to Fly, Dig, or Teleport. The player needs to use Fly to reach Cerulean City. While flying, the exclamation point that usually appears above a Trainer's head when they wish to battle the player will appear. The player then needs to go to Route 24 and, just like in method #1, defeat the Youngster that owns a Slowpoke (with him walking towards the player to start the battle, or the game will freeze). After defeating him, the player needs to Fly to Lavender Town and head west to Route 8. The START menu will appear. Press B, and Mew will appear at Level 7.
(Note: The player must battle the Slowpoke trainer on Route 24, but the player does not have to battle the Gambler in front of the Underground Path. Any trainer will do. One option is to battle one of the two bikers who are next to each other on Route 14, then battle the Slowpoke trainer, then return to Route 14. Because Route 14 is isolated, players should use Repel to prevent running into wild Pokémon in the grass and messing up the trick.)
This method is also known as the "extended Mew glitch" and the "Ditto glitch" due to the involvement of Ditto.
For this method, the player first needs a Pokémon with a Special Stat of 21. It doesn't matter if the stat was naturally leveled or boosted with calcium as long as it's not due to an in-battle special boosting skill. Once the player has this Pokémon, the player needs to find ANY trainer in the game that will engage in battle the moment the trainer is on screen and the player is in the trainer's line of sight. The most common examples are the Gambler east of Saffron City and the Junior Trainer in the high grass west of Nugget Bridge. Often people have already fought these trainers, so other later-game trainers include a couple Bikers on Route 17 (Cycling Road) or the four trainers on the west side of Route 14 (three Bikers and one Bird Keeper). The player then needs to get the trainer off screen. Next, take a single step towards him, enough for him to start the battle, and immediately press START before he spots the player and the exclamation point appears. Once the player has pressed start and the start menu appears, the trainer needs to Fly, Dig, or Teleport elsewhere. The location being traveled to must have a path via which the player can walk both to a place where there is wild Ditto (such as Route 15 east of Fuchsia City) and after to a place with a trainer to fight. This is because the start button will no longer work until after a battle with a trainer (to be mentioned) because the game has been tricked into thinking it's in battle mode. Once the battle with the trainer the player picked was evaded successfully, the player then needs to battle ANY trainer in the game, as long as there is one space between the player and the trainer when the battle is initiated so that the trainer has to walk up to the player and the player doesn't approach the trainer directly. After defeating the trainer, the player needs to find a wild Ditto, and battle it until it uses Transform on the player's Pokémon with the Special Stat of 21. After defeating the Ditto (with any of the player's six Pokémon), the player needs to avoid running into any other wild Pokémon and/or battling any other trainers, and go back to the Route where the trainer the player first evaded is located (for the Gambler, east of Saffron City, for the Bikers, Route 14; etc.). Once the Route is approached, the start menu will automatically appear. The player needs to press the B Button. A battle will begin immediately and a lvl 7 Mew will appear.
This method can be used to catch any Pokémon in the game, even Missingno. in Yellow Version. While a Pokémon with a special stat of 21 will give one Mew, using a Pokémon with a different special stat will give the player a different Pokémon. For example, in the Red/Blue versions, if a Pokémon with a Special stat of 198 is used, a glitch called "LM4" will appear instead of Mew. (See ). There are, however, some glitch Pokémon such as 8 and PkMn n which cannot be caught using this method. Some Special stats will cause glitch Trainers to appear. They may be glitched versions of regular in-game trainers, such as Bruno with Blaine's party.
It is important to note that in the Yellow version, wild Ditto cannot be found at Route 15. Instead, Yellow version players should follow all of the steps above, but instead go to the Pokémon Mansion's basement located in Cinnabar Island. This is because Ditto can be found there in the Yellow version. Also, Yellow version players must bring an Escape Rope, Repel, or a Pokémon with teleport with them to use immediately after defeating a wild Ditto so that the player will not fail the glitch by running into the wrong Pokémon.
20 Glitch Pokémon can be found using Method #3: 10 in the Red/Blue versions, and 10 in the Yellow version. Whenever one of the glitch Pokémon in the Red/Blue versions is traded to the Yellow version (or from Yellow to Red/Blue), it will become an equivalent. For example, LM4 will always become 7g when traded to the Yellow version, even though LM4 evolves while 7g doesn't.
The 20 Glitch Pokémon are listed on the Glitch Pokémon chart. Only 4 Glitch Pokémon on the chart cannot be found using the Mew glitch: 'M, 3TrainerPoké, Charizard 'M, and Q. 'M and 3TrainerPoké would require a special stat of 0, so they cannot be found; 'M can only be found with the Rare Candy cheat, and 3TrainerPoké can only be found by trading an 'M. In the Yellow, Q can only be found by evolving a 44Hy, and Charizard 'M can only be found by trading a Q. If a Pokémon is hacked to have a Special stat of 0, no Pokémon will appear when the B button is pressed.
The glitch in fact works as follows: Any trainer can be used for the first section (Junior Trainer), as long as the trainer notices the player as soon as he/she enters the game screen, and that the player is walking towards them from either the top, left or right (walking from below will not work). Any movement move (Teleport, Dig, Fly) can be used to trigger the glitch, or Escape Rope if in a dungeon. For the Youngster, any Pokémon will do as long as it can be fought without walking up to a trainer. To finish off the glitch, the player must return to the route of the trainer he/she "evaded." The Pokémon that the player will find wild is dependent on the Special stat of the Pokémon the player last faced (wild or from the trainer), and so using a Pokémon with the Special the player needs and finding a Ditto that transforms will produce an identical effect. For the record, the required Special stat for Mew is 21 (This is based on hexadecimal numbers, so one can get the appropriate number for a different Pokémon from a hacking device code list, then translate it to decimal).