There are many ways to improve your odds: a better resume, a great elevator pitch, a knock-out cover letter ... but this one is about working the referral. According to Gerry Crispin of CareerXroad, referrals have a 1 in 5 chance of getting the job. This is a whopping 14 times more likely than a non-referred candidate. You must work those referrals!
To find referrals is not easy for those not connected, but there are ways to generate referrals. For example, let's say you love IKEA (or insert your fave employer here) but you don't think you know anyone who works there. You could use LinkedIn (I am assuming you're on LinkedIn as it's THE place to be if you're looking for a job or hungry to advance your career) to see if anyone you know knows someone who works there. If you have a 2-degree contact, or even 3-degree, you could work an introduction.
Now, you can't just say "hi" and expect a referral. The way to prepare for more success is to use LinkedIn to your advantage. Reply to questions posed, both professional and personal. And post good comments that give the reader insight into who you are, how you work, and your area of interest. I answer questions to do with career management, and in the past have replied to questions or offered my take on holistic health as well, as that's an interest I pursue with some enthusiasm. This ensures that when the potential referree looks at your profile, he or she will read good entries that build trust and a level of comfort in referring you.
Many companies have formal referral programs, where the person who refers a great candidate gets a bonus.It's one of those "win-win" situations.