I have a one word answer for you: networking.
In this day and age, "pounding the pavement" looking for a job is an inefficient waste of time. In my experience it is also utterly useless in finding a job. In 15 years I have rarely ever been contacted by a company that I cold submitted a resume to, and out of those few that called me, none of them ever offered me a job.
Every professional position I have ever held I got through some sort of "connection". I put almost no effort into job searching because I network effectively and use the tools available to me.
My first job out of school was for a major defense company. They had just won a huge contract and were conducting on-campus interviews. I also had three other job interviews before I graduated. All of these interviews were through the school office of career development. Even after graduation, I used the office of career development to land a couple of other jobs. I have also held two positions that I got working through a recruiter.
So here is my advice:
If you haven't done so already, get your resume on file with the career development office at the school you went to.
Talk to professors that you had a good relationship with. Tell them that you are looking for a job. They may have leads.
Do you keep in touch with any former classmates? Are they employed? Tell them that you are looking for a job and maybe they can pass along your resume. This could be a win-win situation, as many companies offer referral bonuses to their employees.
Do you belong to any professional societies? They can also be a valuable network for your job search.
Post your resume on various job sites. HR managers and recruiters are out there every day reviewing resumes.
Contact a recruiter or two.
Are you a member of any engineering networking sites?