You must have a ticket to the magnet train before you can get past the train conductor. To get by him, you need a Train Pass. To get such a pass, you have to already have beaten the Elite Four, and taken the ship to Kanto.
Once there, you can go right to Saffron. In Saffron City, it turns out that Copycat (A girl from the original Red and Blue games, that gives you a TM for Mimic.), has a new house. Visit Copycat, and she'll be whining about losing her doll when she was moving. Your job is to find her doll!
To find the doll, just go to the Pokemon Fan Club in Vermillion City, and talk to the "Clefairy" sitting at the table. Turns out the Clefairy is actually a doll. The man who found it will let you take it back to Copycat.
Go back to Saffron City and return the doll. As a token of thanks, Copycat will give you a Pass to take the Magnet Train. This is how you get past the train conductor to take the train.
EDIT: I forgot to mention the fact that there is a massive power outage in Kanto, and that you have to do another side quest before you can take the Magnet Train. Please just look that side quest up though, because my fingers are cramping up. =P