One of the best ways to focus your job search is to target employers that are most relevant for you, and then make efforts to contact people in the companies and start conversations. Here is an article which describes this approach: http://jobsearchinisrael.blogspot.com/2010/06/employment-networking-target-companies.html.
What do you do when you have this list of 10-20 companies? A part of the action plan can be to do searches on LinkedIn for people that work at the company now (or in the past), and then introduce yourself.
I just heard of another technique that I wanted to share with you.
Create an email for the purposes of employment networking, and send it to the people that you know. The contents of the letter can contain something like this:
I’m looking to make contact with someone at one of these 15 employers:
Do you know anyone in these companies that you could refer me to?
What would you do if you were in my shoes?
Would you mind passing this on to 10 of your friends as well?
Thanks for taking the time to consider this.
You are asking a question about specific companies, so the recipients of your email know exactly what they can do to help. In addition, you are asking them to help take ownership of the process by inquiring what they would do in your place, something that can encourage them to invest themselves. And some of them will pass your message on to others, immediately increasing your visibility outside of your own contacts.
Adding this strategy to support your efforts to target companies may be just what you need to get to new and critical people.