I convinced my sister by showing her Cowboy Bebop ("Ballad of Fallen Angels" always works well).
When I came to college, I had to room in an all-girls dorm, and I only met one girl on my floor that actually watched
anime. She also happened to be the only one that knew that anime extended beyond pokemon and Yu-Gi-Oh. We would talk
about it all the time at dinner, and my other friends would just give us funny looks as we talked about space cowboys,
break-fighting samurai, and wicked awesome witch hunters. I told them they could stop by any time to watch, and they
said they had better things to do than watch childish animation.
My one friend walked in one night when I was watching FMA. It was the episode where Scar had his first run in with Ed
& Al, and blew the hole in Al's armor. She was standing in the doorway, complaining about something, so I held
up my hand to shut her up. As this scene happened, I hear a gasp from behind me. She asked if he was dying, and
she's been hooked since. We're now roommates. We hold anime parties on a regular basis.
That's pretty much how you do it. Find an anime based on their likes and let them watch it. There's just going
to be some stubborn fools that won't watch anime . . .