As you head toward Ilex Forest, you run into your rival, Silver! He'll have with him a Gastly, a Zubat, and the starter pokémon that he stole. With Gastly being a Ghost/Poison pokémon, the best moves to use are ground, ghost, psychic, and dark. Don't use normal, fight, poison, bug, or grass moves on it. The Zubat is the Poison/Flying type, so use rock, electric, psychic, and ice moves on it. Don't use fight, poison, ground, bug, or grass moves on it.

Once Silver is out of the way, you can go into Ilex Forest. A person will ask you to help him catch the Farfetch'd that he lost. To do so, you have to follow it around, using the twigs to make it face a different direction so that you can sneak up on it.

Do this again for the other Farfetch'd that the guy lost. You will get HM01 Cut! This move can be used outside of battle since you defeated Bugsy. Cut can be used when you stand in front of a short tree, like the one that is blocking your path through Ilex Forest right now. Therefore, you will have to teach one of your pokémon Cut.

Once you cut down that tree, you can go into the forest. You will pass by a person standing in an area that you can't reach. Just keep going to the right until you see a path that leads to that guy. He can teach Headbutt to as many of your pokémon as you want. Headbutt can be used outside of battle to hit trees. Doing so might knock down a wild pokémon that you can battle and catch.

Go back to the main path and you will encounter a Kimono Girl. Talk to her, and no matter what you say, you will help her out of the forest. She will thank you and go on her way. She's actually a different Kimono Girl from that other one that you encountered before.

Now you can go to the exit of the forest and head to Route 34.