Chris nailed it on the head for you.
Regarding where game composers got where they are today: Natural talent, practice, studying, Contacts, and Luck/Coincidence.
Seeing that Chris wrote what was on my mind on this topic, I'll just say that if you chose to go into this field, you
better bring
determination and
patience with you. My first composition took about 8 hours total (it was distributed on random days of the week), and it was only about a minute 40 seconds long. It was a solo piano piece in a themes and variations form based off the beginning piano section from Final Fantasy 9's boss battle.
That's another thing, what exactly do you want to learn? Classical? Electronic? Chiptune? Solo Instruments? Jazz? All of it?
I don't want to ask anything further, because it'll end up in a cycle of questions, but it would help a little to know.
Note: Forgot to mention this, but yeah I'm finding that music in movies/commercials/games/television shows aren't really that good anymore.