Hi! Pewter City has a gym, pokecenter, pokemart, and museum. It also has a house with trainers inside that give you valuable information about outsiders. Talk to all the trainers for they can give you tips. Don't try to go too right or a trainer of Pewter gym will stop you and direct you to the gym. The admission fee of the museum is 50 dollars (yen). Inside, you can talk to trainers and read the captions about Mt. Moon and it's moon stones. Now for the Pewter Gym.
Brock is the leader of the Pewter City Gym. Before you go in, make sure all your pokemon are around level 11 and higher. There is only one other trainer inside who is the student of Brock. Fight him and he has two pokemon. If you have either Bulbasaur or Squirtle, put them as your first pokemon in the line-up so they will fight first. The trainer uses a level 11 diglett and a sandshrew. Use Squirtle's bubble or water gun (learned at level 15) or Bulbasaur's Leech Seed or Vine Whip (learned at level 15). If you started out with Charmander, you can use it or any other pokemon except for Pikachu.
Now for Brock. Brock is a rock Pokemon trainer and uses Geodude and Onix at levels 12 and 14.
Like the trainer, use a Bulbasaur or Squirtle. If they are over level 15, this could be very easy because you can use Vine Whip or Water Gun. If you are a Charmander trainer, this could get hard. When Onix uses Bide, use a non-attacking move such as Tail Whip, Growl, Sand attack, etc... To defeat Onix if you are a Charmander trainer, first use Pidgey's sand attack seven times. Then use Rattata's tail whip seven times. Use Charmander's growl seven times. Finally, use any attack you want: Scratch, Tackle, Gust, etc...
When you defeat Brock, he will give you the Boulder Badge, which will raise all your pokemon's defense. He will also give you TM 34 Bide. Read my TM and HM section to find out about those. Bide is a two turn attack. It absorbs the damage given by it's enemy and on it's next turn, hits the enemy back double. It's a pretty good attack when you are fighting someone more powerful than you are. After you defeat Brock, you are finally allowed to go right, past the numerous trainers, and into Mt. Moon.
Heal your pokemon and proceed to the right. You will see numerous trainers there, some are female trainers named Lass, some are bug catchers, and some are junior trainers. I remember that the first female trainer you see there starts with a Pidgey. So put Pikachu as the starting in line-up for that battle. The rest are mainly bug catchers so use a Charmander, if you have one. After you pass that area, there is still one trainer left. She is above a patch of tall grass and she uses a level 14 Jigglypuff. Jigglypuff at that level has Sing, which can put people to sleep, Growl, and Pound. Watch out especially for Sing for if she puts your pokemon to sleep, you will have to switch to another.
Catch pokemon in that patch of grass. You will fight Pidgeys, Spearows, and Jigglypuffs. You will usually fight Pidgeys and Spearows. Do not catch a Spearow there for you can get much higher leveled ones later and they are useless to this point.