The title says it. Did you hear on the radio? Did someone suggest it to you? Did Youtube advertise it? Did you hear it on a movie or a show or a video game? Did you see it in someone's signature of MLK?
I'll list how I found all of mine:
Senses Fail: First heard the song "Can't be Saved" on Guitar Hero III.
Mindless Self Indungence: A family member introduced me to them, the song "Never Wanted to Dance".
The Rescues: From The Legend of Spyro I heard of Gabriel Mann, he produces the music to the games, he sings in the band.
Linkin Park: My mother listened to them all of them time, "In the End" was her favorite.
Evanescence: I really can't remember, but I know my mother loved them too.
Fireflight: A family member show them to me, I actually heard their song "Unbreakable" a while before, though.
All American Rejects: I think it was from that stupid Bionicle commercial, I liked the song "Move Along" so I checked them out.
Blessid Union of Souls: I hear their song "Brother, My Brother" in the first Pokemon movie.
Blink 182: I heard their song "All the Small Things" and "Dammit" a long time ago, recently I listened to "I Miss You" and started listening to them now.
Flyleaf: To be entirely honest, their song "All Around Me" is one of the first memories I have.
Of Mice and Men: I seen their song "Repeating Apologies" on the side of another Youtube video I was watching.
The Story of the Year: A family member introduced them to me, "Until the Day I Die" was the first one I heard.
The Birthday Massacre: A family member showed me the song "The Dream" and then a few more afterwards.
A Day to Remember: I seen the song "You Should Have Killed Me When You Had the Chance" on the side of a video I was watching so I checked it out.
That's how I came across my favorite bands, what about you guys?