Obviously enough the person who gave you the egg gives you the ball.
Honestly, try thinking a bit more next time.
Okay, not really. There is pokedex information to support the fact that pokemon magically appear in pokeballs for some reason. Check Shedinja's dex pages.
People seem to need to be able to explain every little fact of pokemon scientifically. I don't know why.
Think they missed the whole 'Magical Creature' thing?
The PokeBall is given to you by the Day Care Couple, just like in the anime.
This is it, presumably. :<That's what I always figured. In the animé, Ash's Phanpy egg came in a case with a Pokéball attached to the top. I figured that they'd do the same thing for the games, only you don't need a glass carrying case