though I never got mew (had mewtwo, not mew), I don't understand, mew is supposedly in red/blue from what I understand now but I was totally confused at the time and..well, I still am, what's a mew, how does it exist in red/blue, is it legitimate or does it require a really obscure trick to get or..what's the deal with mew? 
Let the guy who knows it all help you all!
First off, here's a picture of Mew:
http://faqsmedia.ign.com/faqs/image/ani151.gifMew is THE most elusive Pokemon in the whole RGBY series. (Note: RGBY stands for Red, Green, Blue, Yellow. These were the versions that came out in Japan and the initials for this generation are concrete to what came out in Japan. Regardless of what you say, it's not changing.) It was (And still is) given away at events, but many did not have access to those events or simply can't afford to go to them.
The fact is that you can give Mew ANY TM and HM combination you want. This fact stands true to this day. It can still learn EVERY TM and HM, and now it can get ANY Move Tutor Move. So it practically knows EVERYTHING.
There was a little joke about how to get Mew, but multiple videos have proven the method to be false. So, for the longest time, all Mew Trainers were seen as cheaters since it was SO hard to get. That is, until one special day.
Near the end of GSC, (Gold, Silver, Crystal for those not in the know.) one person tried one of the most elusive methods ever and actually got Mew. He immediately posted it on GameFAQs.com, but hardly anyone believed it. I was one of the few willing to take the chance.
Here's a few facts you need to know about the trick. First off, in the first generation games, you can pause the game right before a trainer spots you, this means you can then use the HM Fly or use the move Teleport to get away from them. This is what activates the first part of the glitch to pull off the trick. This was changed for the later games, making the trick unavailable in those games.
Second, it needs to be done with a specific combination of trainers. You must pause and then fly away from the first and then battle the second, and NOT lose. The combination of trainers you use render a specific Pokemon. So, in reality, you can capture ANY Pokemon with this method and get EVERY Pokemon without trading.
Third, when you go away from the first trainer, NEVER pause the game until AFTER you face the second trainer. If you do, it will make the trick inaccessible, and could possibly ruin your game, so DON'T do it.
With that in mind, let me tell you how to get Mew. First off, there are TWO specific trainers you must NOT have battled. One of the two is either the kid hidden in the grass right after Nugget Bridge, (The one that says "feat".) or the guy that is right in front of the house that leads under Saffron City and goes to Celedon City. (Either one will work for this trick.) The second trainer is on the Route that leads to Bill's House. He is the LAST trainer looking down before you reach Bill's House. (Note: If the Trainer has a Slowpoke, he's the one.)
Next, make sure you have a Pokemon on your team that knows Fly. The rest don't matter. (And some Poke Balls/Great Balls/Ultra Balls.) Head to one of the two trainers I mentioned earlier and stop right near him. At this point travel in the direction the trainer is facing. Once the trainer is off the screen, move one final step and so that you are right in front of the area where the trainer would spot you. (In both cases, head left one step.) Now, pause the game and save. This way, if you mess up, you can pick up right before you began the trick.
Okay, when you're ready, take one step towards the trainer and IMMEDIATELY pause the game. (You MUST be quick at this.) If you are successful in getting the screen up, pick Pokemon and choose the one with FLY. Choose to go to Cerulean City. (Where you battled Misty.) If the trick worked, when you fly away, the exclamation point will appear above the trainer, but he won't battle you.
When you land in Cerulean, head up through Nugget Bridge and towards Bill's House. Find the kid that's facing down that was mentioned earlier and battle him. Make sure you ONLY battle him during this part of the trick. You battle anyone else, you won't get Mew. Note that, you must NOT talk to the trainer, the trainer must WALK to you and he must walk at least ONE step. Otherwise, it won't work. Beat the trainer.
After you win, Fly back to the town before the first trainer you went to. (In the case of the Nugget Bridge Kid, Cerulean City. In the case of the guy next to the House, Lavender Town.) Now, head towards where the first trainer was. At some point, (Most likely right when you enter the route.) the pause screen will pop-up automatically. Press B. (Don't do anything else. You'll ruin the trick otherwise.)
After you press B, a battle will begin and Mew will appear. Now you just have to catch it.
After you catch it, you can safely Save the game. Mew is officially yours.
Hope that helps. Best of luck if you dare to take on the mission.
