Network Network Network

There are plenty of employers who say they have jobs but don't. There are some jobs that exist that employers don't tell the world that they have available. And many of the publicly available listed jobs have already selected their candidates but are just filling a company policy requirement that all jobs be posted. Of people placed into jobs, some ---- but only a few ---, are placed through a want ad and search process. Don't cut yourself off from the listings by any means. But the less you have to rely on listings, the better you are likely to do.
Networks are the way to go.
And the biggest and best network is Linked In.  http://www.linkedin.com/
If you are searching for a job, you owe it to yourself to create a profile. There are groups you can join that are about your specific area of expertise. A greater percentage than usual of the jobs that are listed are real searches.
Are you part of a professional organization - even one that you joined as a grad student? Reconnect as soon as possible, particularly if there is no cost to doing so. National organizations in your area of expertise often maintain online job boards. As a general rule, there is no cost for group members to search these. As a general rule, searchers pay for their listings or alternatively, use up a limited number of free listings. This keeps the number of listings down to those that are genuine.
If you have other suggestions, please post them in comments.