To unlock the mini game hidden within Pokemon Yellow called Pikachu's Beach all you have to do is get a Pikachu that knows Surf. Currently there are three ways to do that and they are; win Nintendo's "Get a Surfing Pikachu" contest, use Gamshark to teach Pikachu Surf or get a Surfing Pikachu through Pokemon Stadium (go to the Pokemon Stadium Cheats and Codes section).
When you have one, all you have to do is go directly south of Fuchsia City and go inside the house near the lake and talk to the man inside. He will be amazed you have a Surfing Pikachu and will let you play the mini-game "Pikachu's Beach".
So what is Pikachu's Beach like? Well all you do is push left or right when going over the waves to do flips in the air. If you don't wipe out when you hit the water you'll get 50 points for one flip and 150 points for more than one. If you look in the lower right of the screenshots you'll see a HP counter, which acts like a timer and is constantly going down. Whenever you score points, the points are added to the counter, so the more flips landed the more experience your Pikachu will earn when it reaches the shore.
Once you think you've earned the highest score you can get, the Gameboy Printer will allow you to print out your score to amaze all your friends of your surfing ability! That's about all that this mini-game is. It's not much, so if you don't want to sacrifice your Pikachu you don't have to, but it is up to you.