
Pallet Town
This is where you begin. You start in your room, where there is a PC. Go check it out and WITHDRAW the Potion. It will come in handy. Journey to the grassy area north, and Prof. Oak will drag you back to his lab. You will be given the choice between 3 Pokémon, Bulbasaur, Charmander, and Squirtle. No matter what you choose, your rival Gary (or whatever you named him), will pick the Pokémon that has an advantage over yours.
Your Choice - Gary's Choice
Bulbasaur -- Charmander
Charmander - Squirtle
Squirtle --- Bulbasaur
After you select your Pokémon, you will battle Gary. Be sure to win, so you can gain a little experience and score some cash. Both yours and Gary's Pokémon have about 2 moves. 1 is Tackle, and the other is a move that lowers defense or attack. Use use the basic attack, that should kill Gary since he usually wastes his time on the attacks that lower defense or attack. Once you win/lose against Gary, go to his house (right of your house), to get a Town Map from his sister. Now, you will set off to Viridian City, by going north through Route 1.
Viridian City
The PokeMart has something for Professor Oak that you need to bring to him. It allows you to use the Pokedex and allow you to play linked games or trade. Bring Oak's Parcel (that's the item) back to Professor Oak in Pallet Town. On the way back, you can catch two Pokémon, Pidgey and Rattata... Now, go back to Viridian, buy whatever items you feel is neccessary from the Pokemart (just some pokeballs, potions, and maybe antidotes) and go through Route 2 to get to the Viridian Forest. (Gary is in Viridian City too...just go left of Viridian City and you will find him...and a small pach of grass where you can catch Nidorans and Spearows.)
Viridian Forest
Here, you will face many trainers. Don't worry, this can be a good thing. It builds up experience real fast, and you can catch Pokémon while your here. Building up levels too fast can be bad too, since they won't obey you early on. If you bought Pokeballs, you can capture some ok Pokémon. Depending on what version, you'll either get a lot of Caterpie/Metapods or Weedle/Kakunas and less of the other. If you're lucky, you can find a Pikachu. (Pikachu is really really rare..... I takes a lot of patience to find one.... Just wander in grass and fight waves of caterpie/weedles untill you finally see a pikachu... it took me about 30 minutes untill I finally caught a Pikachu)
Pewter City
Here is the location of the first Gym. The trainer here is Brock. He uses rock-type Pokémon. If you chose a Squirtle, you'll win fast. Bulbasaur does pretty good too. Charmander isn't effective when you use Fire attacks on rock-Pokémon, so over level him or use other Pokémon. Defeating Brock will get you a Boulder Badge, which will let you use FLASH any time and raises the Power of all your Pokémon a little.
Note: When a badge lets you use something like FLASH or CUT, it doesn't mean you can use it right away. You need to find a Hidden Machine (HM) that teaches that ability. Use it to give that ability to a Pokémon and THEN you can use it.
There are several things to do in Pewter. Pewter is one of the few cities where you don't have to do anything to get out of that city, in order to get to the next one. It's a good thing to talk to everyone, explore suspicious areas, and check our all the buildings. As in every RPG, it will usually end up with you getting rewards and freebies. When you're ready, take Route 3 to get to Mt. Moon. If your Pokémon are in bad condition, use an item to heal them. If you are cheap (like I was), you just have to make the trip back to the Pokecenter in Pewter.