In the highly competitive field of the art world, writing a smart, snappy and unique cover letter will make you much more competitive in the applicant pool. The key to writing a good cover letter is to highlight your experiences, education and personal strengths and let the gallery know why they should hire you. Essentially, a cover letter is an advertisement for you as an employee and should convince them to read your resume fully.
Start with an introductory paragraph which, like an academic paper, should have a thesis statement that you prove within the body of the letter. Make a bold statement explaining why you are the best candidate within the first three sentences or you run the risk of boring the Gallery Director.
In the second paragraph, describe an experience or two that illustrates ways in which you have exercised the qualifications you list in the introduction. For example, you could say that as a gallery intern, you utilized Photoshop on a daily basis.
When writing the closing paragraph, restate your thesis using difference words, while adding that you feel that the position would help you in some way. You may also wish to include a bit of knowledge you have pertaining to the gallery, such as the artists they represent.
Make sure you ask them to review your enclosed or attached resume or they may not bother to look at it. Then thank them for their consideration.
Most importantly, be sure to proofread your cover letter prior to sending it out. By reading it aloud, you will be able to easily spot typos and edit awkward phrases.
Be sure that the tone of the cover letter is confident without being overly boastful.