Karen Cheng has a blog post up on this subject that is getting a lot of attention. Her advice is pretty sound if you can get past the fact that she uses The Bachelor as a metaphor for her advice.
Shorter Karen: if you have no connections you need to make them.
Here’s a comment on the post from Wisty on Hacker News that I thought got to the heart of the job search connundrum:
Everyone with a job knows a hiring manager, and the hiring manager will trust them more than all the job seekers banging on their door.
This might fail if you want to work for Apple, Facebook, Google, Microsoft, etc. I've heard Apple employees tend to get stalked a lot by people who want to work for Apple, so they've got the same kind of defences that hiring managers have. You'd probably need to really stand out to convince them you're the kind of person they should introduce to their boss. But these companies already have pretty active recruitment. You want to target the companies with poor recruitment (i.e. most companies).
Most companies kind of know they need more staff, but can't be bothered going through the process of advertising, weeding out hundreds of unqualified candidates, then having to pick between the 2-3 good candidates who get on the shortlist. It's almost as stressful for them as it is for the applicants. If a good candidate presents themselves before they've bothered advertising, they'll often take them without bothering to advertise (expensive), weed through the chaff (time consuming), and picking from the shortlist (stressful) ... all of which creates the risk that they'll either not find the right person, or hire someone who doesn't quite fit simply because they felt they were the best of a bad bunch. And if they don't like you, it's easy enough to say "sorry, no positions are currently available".