You get the Johto starters after you beat the Elite Four. If you go to Route 101, Professor Birch will be attacked by a Shroomish, like he was attacked by a Poochyena at the start of the game. He'll give you a starter if you help him.
Once you've beaten the Delta Episode, do the same thing again. The same thing will happen, except the professor is attacked by a Machoke and you'll have to choose from Unova starters.
Finally, you'll get the Sinnoh starters once you beat the Elite Four a second time. The cutscene where the professor is attacked is actually quite humorous, so I won't spoil it.