How to get a Mew in R/B:
In Vermilion City go on board the SS. Anne as usual! Then once you have the HM cut, fiht a trainer in one of the rooms, and lose to them. You will end up in the Pokemon Centre and the SS. Anne won't have departed! Now Play through the game until you get HM Surf and HM Fly and HM Strength. Now teach all three to Pokemon. Fly to Vermilion and the SS. Anne will still be there. Now surf around the SS. Anne and round to the back. You will see a truck. Use strength on the truck and move it. A Pokeball wil be underneath it. Hit A Button at the Ball and Mew will appear.