Hi! Before you go in, make sure you have changed your pokemon box to an empty one in the computer. As mentioned before, Safari Zone is a big park with lots of rare pokemon to capture. It is located at the very top of Fuchsia City. To get in, you have to pay 500 dollars for admission. This is a very good deal because you will get 30 Safari Balls. Safari Balls are like Pokeballs except they can only be used in the Safari Zone. You will also get 500 steps. That is, after you have walked 500 steps in the Safari Zone, the announcer will tell you your time is up. Don't worry, you can get in again. If you still have steps left but want to leave, go out the entrance, or fly or teleport away. When you are engaged in a battle with a Safari Zone pokemon, you have four choices: Throw Safari Ball, Use Bait, Throw Rock, or run. Throw Safari Ball is to capture it. Use Bait is to distract it. Throck rock is to weaken it. And run away is to leave the battle. Do not use too many bait or the wild pokemon will run away. Throwing rocks will sometimes drive them away, as well. My advise to you is to just use 2 bait or so, and keep on using Safari Balls, one after another. For big pokemon, you could use rocks. There are four zones in the Safari Zone. Each zone may contain some new pokemon, so go in every patch of grass you see in different zones!
There is also a Secret House in the fourth zone. If you reach the secret house, you will be rewarded with HM 3, Surf! Surf enables your water pokemon to swim around in areas of water. You will need this to get to Cinnabar and Seafoam Island. You cannot use this HM outside of battle yet because you have to beat Koga, the Fuchsia Gym leader first. Follow the pictures below to get to the Secret House. Descriptions of each picture are right underneath each picture.
By the way, I remember that you can only catch Chansey and Tauros in the third zone. You can catch Scyther (red) and Pinsir (blue) in the first zone. The other pokemon are scattered about.