Try a good job portal. Most companies post openings their. Sending them letters will not help since some might not have openings and will just ignore your letter.
Prepare a good resume and a cover letter and search the job portals for the kind of job and the kind of place you are interested to work in and post your resumes to those companies. Your chances of sucess will improve and also register your resume on some job portal that way head hunters will be able to find you and offer you jobs.
I have registered in quite a few job portals a year back to get a job which i did in a week and even now i keep geting offers from various companies from all over the world. My inbox is littered with job offer emails.
And always target big companies, the chances of your growth are better in a big oraganizatons than a smaller one though the smaller one might be much easier to work in. Give good attention to your resume, do not make grave errors in them cause you will be judged by the way you present yourself rather than the knowledge you posses.
I am a bussiness and commerce grad and did my Phd in Human Resource and Business Taxation. I also have a Diploma in Web Programming, PHP, MySql and .ASP. But nobody cares about that as long as i do not present myself good.