I'm not an animator, so can't really give you an specific tips - but my general advice would be to showcase your work as much as possible, get it out there on a funky-looking website, take part in different digital communities, and network with the right people.
I don't know if there's something equivalent specifically for animation, but I really like browsing Dribble when I need inspiration for digital or web design ideas.
Make use of social media to promote your latest animation project (Twitter, LinkedIn and Google+ are good for connecting with other professionals), and you'll soon see people commenting and taking notice of your work.
Also, going to gaming expos and conventions, meetups (I use meetup.com to find relevant meetups in my local area).
Generally, people in creative industries are always on the look out for "hot new talent", so in most cases you just need to make a name for yourself and devote some time to "marketing" yourself and it will pay off.
Where can I check out your work incidentally? I would love to see it!