The cover letter is your opportunity to connect with a particular employer and give them a good idea of who you are. Unlike your resume, the cover letter is your chance to tell the employer what you can do for them, and what you want from them. You should also remember that your cover letter demonstrates your writing ability - what do you want the employer's first impression to be?
The first paragraph of your cover letter should identify you and explain why you are writing. Generally, this paragraph should let the employer know that you are an attorney, which law school you attended, and for which firm or organization you are currently employed. The most important piece of information to include in your first paragraph is that you are interested in a position at the recipient's organization. If you are being referred for the position by a mutual contact you should mention this in the opening paragraph. Personal references are generally viewed as an important and compelling factor when potential employers are determining who should be interviewed, so be certain to indicate if you have one.
The middle paragraphs of your cover letter should go into some detail about your work experiences that are relevant to the position you are seeking. Good middle paragraphs are like stories that unfold for the reader and will paint you as someone who belongs with the reader's organization.
An important and often overlooked factor of middle paragraphs is that you must focus on what you bring to the table. An employer reading your middle paragraphs will be thinking to themselves: "What can this person do for me?" You need to answer this by distinguishing yourself from others with your unique skills, personalities, and experience. How you master this is something that will have a definite impact on whether or not you even get an interview.
You should use this section to provide information about your background and skills. Using the space to simply reiterate the contents of your resume would be wasteful, however. Instead, you should use this space to add depth and detail to the experiences that are most relevant to the position. Focus on the skills and qualities that the potential employer would find most useful. Doing so will help establish your understanding of the position in addition to presenting you as a qualified candidate.
This is also an opportunity to express your reasons for being interested in the company and position. This is another opportunity to connect-the-dots between your experiences, motivations, and the position. The cover letter itself is evidence of your abilities. Present your arguments in a clear and compelling manner. Be certain to double check spelling and grammar.
The final paragraph of your cover letter should thank the employer for their consideration and stress that you are interested in speaking with them about working for their organization. As discussed above, the middle paragraphs are the most important in terms of making your case. If your final paragraph is a well written conclusion, the employer will feel the need to contact you.