Even if you already fought that trainer with the level 17 Slowpoke, and the swimmer in the water at Misty's gym(which also gets you a Mew), you can still get it. But you need to save the trainers that can initiate the trick. Such as the trainer standing in the grass next to Nugget Bridge, the Gambler east of Saffron's gate or even one of the swimmers south of Fuscia. Mew's decimal number is 21, so you will need a pokemon with a special stat of 21. Just do as Charizard Fire God said, and press start, but here's where it's different.
If you're playing Yellow, make sure you have an escape rope and fly to Cinnabar. Go in the Burned Down Mansion, and go to the floor where you get the secret key. You have to walk infront of a scientist a few steps up from him so he walks up to you. Once you beat him, look for a Ditto. When you find one, switch out your pokemon with a special stat of 21. Then let Ditto transform into it so it's special is now 21. Run, use an escape rope so that you don't run into any pokemon. If you do it'll mess up the glitch. Fly to Lavender Town and walk west, start will appear, and press b. Wild Mew appears.
If you're playing Red/Blue, fly to Fuscia City. Walk out the east gate and walk a couple steps infront of any of the trainers. battle, win then walk into one of the patches of grass. Same as yellow, search for Ditto, let it transform in the pokemon with a special stat of 21, then run from the transformed Ditto. Fly back to Lavendar and walk west. Another wild Mew appears.
Mew is not the only pokemon you can obtain by doing this glitch. You can get anyone you want. Even Missingno. in yellow. For a complete Hex list on all the pokemon go
here.
For this list, just look at the numbers which are situated in the column called, "Decimal(Special Stat for Mew Trick)".
You can get all the pokemon you want, even the ones unavailble in a certain version. They will all be at level 7 when you get them, so you can trian them yourself to be stronger than they would normally be. Have fun with the list.:)