There are usually far more actors than there are acting jobs. Therefore, actors usually spend a great deal of time preparing for auditions, practicing monologues and perfecting their audition packet. This includes a resume, cover letter and head shot. In order to make the best first impression, you must construct a cover letter with great care and include several sections.
Providing a Proper Introduction
The greeting and first paragraph of your cover letter are the first impression casting directors have of you. Make sure you have a formal salutation and no spelling errors -- it's crucial. The introduction should state your interest in the production you are auditioning for and why you are fit for the part. Ideally, you'll already have a relationship with the recipient of the cover letter, allowing you to remind the casting director of your prior connection in the first paragraph.
Highlighting Relevant Skills
Much like cover letters for 9 to 5 jobs, cover letters for a theater audition need to include relevant skills. Mention classes you've taken, productions you've appeared in and what hobbies or interests may qualify you for the role you want. A side job as a model may not be directly related to theater, but the skills learned while doing it may prepare you for the audition.
Mention Previous Roles
Note other auditions you've nailed and roles you've performed. This lets casting directors see that you have the experience to excel in another role should you do well at the theater audition. It also shows that you are a theater professional in demand. If you haven't yet performed, mention a relevant award you won or a callback you've earned. Lastly, directors and talent scouts will feel comfortable knowing you understand what hard work and commitment theater jobs entail, based on your other acting jobs.
Show Your Dedication
Show casting directors that you've gone above and beyond by researching the production and characters. Give a brief description of how you interpret the production's meaning and characters' motivation. Consider referring to a theme in the play that resonates with your personal life. However, keep in mind that casting directors are usually very busy, so the section describing your understanding of the production and characters shouldn't be more than a few brief sentences.