Now that you have captured/fought your game's legendary, you can move on to the next stage of your journey: fighting the Elite Four and League Champion! To do that, go back to New Bark Town, and surf east. After arriving in Kanto, you can go into Tohjo Falls after that, and use Waterfall to get through the cave.
Along the way you will find a house where a book tells you where to find the Day-of-the-Week Siblings.
You will fight many trainers along the way and will eventually get to a house where a woman will heal your pokémon for free! She will do this however many times you need, so this is a pretty good place to train up. However, if your pokémon are somewhat low in level, you should probably go elsewhere to train, until they are levelled up to around the level of those in this area of Kanto.
At the end of the route, you find Victory Road, a cave where you will need Strength. When you get to the end of this area, you encounter Silver!! I will add more information about how to defeat his team here.
Beyond Silver, you can go outside to Indigo Plateau, which is like a Pokémon Center along with a Gym of sorts, where the Elite Four and the League Champion are waiting for your challenge. You can get pokémon from your PC Box now, and you can use a flying pokémon to go back to Johto. If the Johto locations are greyed out, you should find a way to go west so that you are closer to the greyed out symbols. They become grey if you are too far away from them for your pokémon to fly to.
Read on to find out which pokémon to bring against the Indigo League.