In crystal it is to the right of vermillion city, which is the place you arrive when you get off the S.S Anne.
To get to it, you have to awaken the massive Pokemon blocking the way (Snorlax) by switching on your Pokegear and tuning it to 'Pokemon Sleep' or something like that.
Then if you click on the Pokemon it will wake up and battle you.
Then catch it or defeat it, and you will be able to get into diglett's cave.
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sorry,but going thrugh digglet's cave is the only way
Some Gym Leaders leave their Gym periodically, as a time to gain their Phone Number after you have beaten them. Brock goes to Digletts Cave everyday from 12PM to 3PM, so try challenging him at a time other than those.
You have to go to the S.S Anne which will drop you off at Vermillion. Then you will see (to the right of it) there is a massive Pokemon blocking the way to a cave. That is diglett's cave. To get into it, you have to tune your pokegear radio to Poke Flute and it will wake up the Snorlax and attack you. All you need then is to either beat it or capture it (probably the best option as its not going to appear again) and then it will leave you with the entrance to Diglett's Cave.
any day between 12 & 3
Digletts are the only Pokemon in Diglett's cave but they appear so often that when you take your first step into the cave that there is a 7 out of nine chance a Diglett will appear