In the Kanto region, go above nugget bridge. You will see a man standing in the middle of the ledges. He will say He hasn't been a very good trainer. He will then ask you if you want the Charmander.
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The only way to obtain a Charmander in Generation II (Gold, Silver, Crystal) is to trade one from another game.
Well, honey, in Pokémon Crystal, you can't catch Charmander. You'll have to trade for it from another game that has Charmander, like Pokémon Red, Blue, or Yellow. So, either make some friends with the older games or hit up the trading forums online to get your fiery lizard fix.
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You can't catch a Charmander in Pokemon Silver. You have to trade it from the original games.
Trade a charmander from firered or leafgreen to emerald.