1) In my opinion, your application should always include a real, personal cover letter, even if the application guidelines don’t require one.
2) Your writing sample should represent your strongest work to date, and should adhere to guidelines about length and formatting. I, for one, prefer double spacing for fiction and non-fiction. Guidelines on length may differ from class to class, but in most cases, five to ten pages of writing suffices to show me your work’s merits. If you are applying to more than one class, consider tailoring your writing samples to the individual courses. For an upper-level workshop in a genre, it might, for example, redound to your credit to submit a sample in that genre. But if I had to choose between “best work” and “work in x genre,” I’d always prefer that you show me your very strongest writing, regardless of genre. Submit work that showcases your voice, your interests, and your dedication to the craft of writing. I think all writing teachers prefer a shorter, stronger application to one that reaches (or exceeds) the maximum number of pages allowed but varies in quality.
3) If you’ve missed the deadline for applications, there may be no way to get into the class in question unless there has been an extenuating circumstance. Different teachers feel differently about deadlines, of course; it might be worth trying your luck. I tend to believe that if many tenable applications have been submitted on time, it would be unfair to all those students to give preference to a late application (on which the applicant has had more time to work).
4) Make your note to the professor polite and professional, particularly if you’ve never met him or her. You might be surprised at how much more effective a note addressed to “Dear Professor X” can be than one addressed to “Hey!” On a related note, make sure you use the correct name for the professor, and that you’re spelling it correctly. (This may sound obvious, but in a recent round of applications I considered, I got one application addressed to “Dear Professor Cork.” I would never disqualify an application for such a small-scale mistake, but when you’re trying to make a good impression, everything you do right counts.)
5) Honesty is more helpful than fatuous praise. (This is just general life advice. Most of what I’m writing here is.) Telling a professor that you’ve “heard good things” about her class, or that you’re “in awe of” her work, smacks of flattery. If, however, a specific friend spoke well of a professor’s class, you might mention that; if you’ve read a professor’s book and something about it makes you want to study with her, say so. If you want to take a workshop and don’t know anything about the professor, it’s fine just to say that you’re eager to learn about the subject matter.
6) Read the syllabus, if it’s posted. Professors work hard to craft strong, engaging, innovative syllabi. An application that responds to the syllabus (by expressing legitimate interest in its subject matter or methodology, for example) helps the instructor understand why you’re interested in taking this specific class at this time.
7) When crafting your letter of application, try to let the professor know what makes you unique as a person and writer. Are you a student in the sciences who’s never tried writing before but passionately wants to? Is there something about your interests, background, experience, or influences that might give you a unique perspective in workshop? Are you hardworking, persistent, eager to learn about revision but unsure where to begin? Those things are interesting and make you stand out. In letters of application, students often claim to be monomaniacal about writing—most letters, in my experience, declare that the applicant has been writing since first grade, or something of this nature. (Not an uncommon circumstance, in a culture in which we take cheap, readily available paper for granted.) Those things may be true, and you can mention them if they are; but also remember that a professor may wish to admit a diverse group of students to allow for lively discussions. If your letter is honest, straightforward, and expresses something about your particularity as a person, this helps her to do so.
8) Also remember that anyone who devotes herself to her own writing is likely an avid reader of other authors. What current or canonical writers capture your imagination, and why? A writing instructor may be more eager to teach a room full of students she knows to be excited about, say, George Saunders, Colson Whitehead, Lucretius, Zadie Smith, Deb Olin Unferth, Edmund Spencer, Deborah Eisenberg, and Felicia Luna Lemus than a room full of people who have always really, really wanted to be writers.