The daycare is on island 4. some Pokemon won't breed however.
for more info:
http://www.serebii.net/pokedex-rs/
Charmander is a fire type of Pokemon. To get a Charmander egg in Pokemon FireRed, you can breed Charizard with Ditto.
from Pokemon FireRed
he hatches
My mom
Here is the fastest way possible: Have a Pokemon that you want to train be traded to you from a different game that will make the Pokemon receive boosted exp points plus if you have it hold a lucky egg you will receive even more exp points. Lucky egg can be obtained by catching lots of chanseys.
Chikorita cannot be caught in Pokemon FireRed. However, you can catch a Bayleef in Pokemon Colosseum, transfer it into FireRed, and breed it to get a Chikorita egg.
beat the Pokemon league and go to 4 island and breed two compatible Pokemon and BAM! you have an egg
8.
you need a ditto and a rainbow ticket then go to the fourth island and go up to a daycare center and put the ditto in and another Pokemon but not legendary Pokemon and wait a little while when the man steps forward you will receive an egg.
Breed eltabuzzs and hatch the egg
leave 2 Pokemon in the day care center and they might have a egg
It will probably freeze you game