Instructions
Enter any town and purchase Elixers from the PokeMarts, which can be used in combat to heal your Pokemon.
Head to a PokeCenter in any city and speak with the trainers there. They will heal or revive your Pokemon free of charge, and also remove any negative status effects on them. You can also exchange the Pokemon you are carrying here, putting the rest in storage.
Take your Pokemon home, at the start of the game, and you can fully heal your Pokemon there.