First off - the difference between a CV and a resume: a resume is shorter. Seriously, that's it. A CV is used to apply for academic positions, while a resume is usually more appropriate when applying for jobs outside academia. CV stands for Curriculum Vitae - which is Latin for 'job experience from kindergarten'. In contrast, the resume needs to be deliberate and focused in its delivery of information. Less is more. I keep versions of both.
Length of your Resume/CV: for University job applications, a few pages is OK. For anything else, fit it on two pages or less. I also tend to tailor each resume to each job I apply for. It's time-intensive, but well worth it in the long run.
To begin - look at who you have studied with, what degrees you have earned, and your experiences in your chosen field. Compile information on what you have participated in: masterclasses, competitions, summer festivals. Any awards, scholarships, or assistantships? Did you accompany any choirs, vocal and instrumental studios, recitals, opera scenes, operas or musicals at your university? Did you have other performing related jobs, such as a church gig, jazz group, or a high school choral gig? Do you have a private teaching studio? Ideally, professional experience will replace experience earned as a student ('college experience') ASAP - but to start, you go with what you have.
Some articles - Musician Wages has this article on musician resumes. Eastman's Resume Handbook for musicians. Berklee School of Music has an online resume tutorial.
You also need a basic cover letter. Here's Eastman's Cover Letter Handbook for musicians. Also Cover Letter Samples and Cover Letter Tutorial from Berklee School of Music. They are all good ways to get started. Here is some cover letter advice from Insidehighered.com.
Finally, you should have a demo CD of your playing. Record your recitals! Ideally, you will have recordings of a variety of repertoire: arias, art song, instrumental literature, choral, and pop/broadway.
You may also need a DVD of your teaching, depending on what job you are applying for.
In many circumstances it is helpful to have a repertoire list. Compile all of the repertoire you have performed. I keep them in these categories: art song, opera, instrumental repertoire, musical theatre, and choral repertoire. Further formatting and grouping of these lists (which becomes necessary, the more repertoire you amass): I like to do my instrumental rep by instrument group, then composer (Strings - Mozart, piece; Brass -Strauss, piece). Some people group their art song according to language, others by composer. Use whichever has the strongest presentation. When formatting, try getting as much info on one page as possible in an elegant, clear way. For example, list your rep using two columns instead of one.
Some job-search advice from a Prof who has been on multiple job search committees in South Carolina.
*Always check if the position has been advertised in the past 5 years. Some positions are vacated quite regularly = red flag.
More to Come, as I think of it . . .