Connecting to people already working in the company really helps. Pitch yourself to them and they might agree to provide you with an internal referral: it's an excellent way to jump the queue in the hiring pipeline.
Referrals are (or should be--I know some will refer any and all for the referral bonus) really intended to refer someone you have some first-hand experience with. I'm going to refer someone out of the blue to the company job site.