Your final challenge is to prove your skill as a trainer by defeating the Pokémon League's Elite Four. You won't be seeing a Pokémon Center or a Pokémon Mart for a while, so stock up on items before you leave Viridian City. Head west out of the city and follow Routes #22 and #23 to the Pokémon League headquarters.
Onward to Victory (Road)
With the Earth Badge in your possession, nothing's stopping you from entering the Indigo Plateau, the challenge grounds of the greatest trainers of all, the Elite Four. The path there is through Routes #22 and #23, but first you'll have to fight your other nemesis: Gary.
Gary's not going to let you just march up and challenge the Pokémon League without a test. His team is wildly varied in all versions, so you'll have to match each of them with effective Pokémon. If possible, bring a team of high-level Pokémon from each of the following types: Fire, Water, Electric, Ground, and Ice. After you defeat him, go back to the Viridian City Poké Center to heal. You'll need all of your strength for Victory Road.
One final route
There isn't a whole lot to say about the very last route in the game. Route #23 is long, and you begin at the very bottom. You will need to bring a Pokémon that knows Surf. Except for Ditto in Red and Blue, you won't encounter any Pokémon that you didn't encounter early in the game. So if you missed Ditto before, now's a good time to catch one. Otherwise, make sure that you're fully equipped and don't forget to bring plenty of Ultra Balls that you will need in order to capture the final Legendary Bird. Victory Road is next.
There are three hidden items on Route 23: A Max Ether on the island in the middle of the water, an Ultra Ball on the rightmost boulder sticking out just after you reach land again, and a Full Restore to the left of the very last patch of grass.