To get the Exp. Share in FRLG, you need to talk to Oak’s Aide on the top floor of the gate located east of Fuchsia City. He will give you the Exp. Share once you’ve caught at least 50 different kinds of Pokémon (this can include Pokémon you’ve evolved as well).
Once you have 50+ Pokémon caught and showing in your Pokédex with a little Poké ball icon, then head to Fuchsia City and chat with Oak’s Aide to get your free Exp. Share.
The only prerequisite to getting the Exp. Share is catching 50 Pokémon.
Luckily, you get the Exp. Share right next to Fuchsia City, home of the Safari Zone.
So if you haven’t gotten the chance to catch a lot of Pokémon by this point in the game, you can make a quick stop there and pad out your Pokédex.
How To Reach Fuchsia City
I’m assuming that if you have 50 Pokémon then you’ve probably made your way to Fuchsia City already – but just in case you haven’t, I’ll break it down here:
Step 1: Head west from Celadon City until you reach Snorlax.
Step 2: Play the Pokéflute to wake Snorlax up and get into the building on his left.
Step 3: Walk through the gate (requires that you have the Bike) and ride down Cycling Road.
Step 4: Ride all the way to the bottom of Cycling Road, then head east and cross through the gate on Route 18.
On the other side of this building, you’ll be in Fuchsia City and be able to get your Exp. Share.
How To Reach Professor Oak’s Aide
Once you have enough Pokémon, here’s where you’ll find Oak’s Aide and get your Exp Share:
Step 1: Head to Fuchsia City, and then walk east until you reach Route 15.
Step 2: Walk inside of the guard building on Route 15.
Step 3: Walk up the stairs inside of the guard building.
Step 4: Talk to the man in the lab coat (Professor Oak’s Assistant).
Step 5: When he asks whether you have 50 Pokémon or not, say “Yes”.
If you do have 50+ Pokémon (I know you’re not a liar), then he’ll hand over the Exp. Share, which you can then give to any of your Pokémon as a held item.