Not much will happen on Route 1, but it mainly serves as a pathway into Viridian City. Simply make your way north
by zig-zagging up through the tall grass until it clears.
Route 1 isn't the ideal place to catch a Pokemon, although it can be useful for training. You can walk back and
forth through the grass to fight Pidgeys and Rattata's to level up your Pokemon.
You can also find a Potion (which will heal your Pokemon by 20 HP) from the first person you see.