List and bring attention to everything you're including with the letter, in order.
All this effort is for naught if your reader doesn't go on to look at your resume and any other documents you've included.
I am a proficient computer and Internet user and am familiar with Microsoft Word. I would consider my strengths to be my written and verbal communication skills, my high attention to detail and my ability to always be well organised.
I am a hard worker with an enthusiastic attitude and a loyal disposition.
Check for typos—they'll jump out at you more readily if you go back to it cold, perhaps the next day, not right after you wrote it.
Check for grammatical mistakes and proper punctuation.
Support your statements with evidence whenever possible.
Don't merely assert that you're a skilled writer. Mention that you won two legal writing competitions and have published over 100 articles.
Use your closing paragraph to thank the firm for considering your application and tell your reader why you would make a good addition to his team.
Explain how your background, skills, experience, and past achievements make you the perfect candidate for the job. Indicate how and when you'll follow up on your cover letter and be sure to mention the best way to reach you.