Be direct, express an interest in the company and wishing to be a part of it. If seeking a job that has been advertised, make specific reference. Mention the skills that have a connection with the job. You can mention other interests in a separate paragraph.
GIve a one paragraph history of your experience and credentials. Attached the complete resume. (As the attached resume shows, I have...)
Keep it to one page, use a standard type face (Times Roman is best). Check and recheck for spelling and grammar and have someone else check it for you.
I spent two years looking for work and gave up. Being 60 when I started the search I ran into the "over qualified" for the job, or not skilled in the latest technology. Also, my unwillingness to relocate and the fact that I only had two jobs in the previous 35 years worked against me. Now the trend is to stay on one job four to six years and move on to something else. I liked my job, it paid well. The benefits were good. For 22 years it was a great job. New boss comes in, and I go out. Was not fair, but that is how it goes.