Cover Art Designer - Graphic Design Specialization:
A cover art designer is really simply a graphic designer who happens to focus on music related projects. Often, designers who work on cover art and liner notes also dabble in designing posters, t-shirts and other merch for the artists with whom they work, although not all do. The extent of a designer's input into the finished album artwork and liner notes can vary greatly from job to job, depending on what the musicians and/or label wants.
The person hiring the designer determines the extent of the work that needs to be done on each individual project. Sometimes, a label or the musicians will have a very specific idea of what they want on their album cover - they may have a photo or design in mind and they may have predetermined everything from font to color. In this case, the designer is in charge of laying out the band/label's vision and putting it into the proper format to be delivered for manufacturing.
In other cases, the designer may be asked to come up with a design from scratch and then will work with the band/label to settle on a final draft.
Finding a Job:
Many designers who work on album cover art work on a freelance basis and are hired on a per-project basis. If you want to work as a freelance designer, you may find you have to start out designing a few album covers for free to build up a portfolio of work. Once you get started, if people are pleased with what you're producing, then you will likely find that most of your work comes to you through referrals.
Not all designers are freelancers, however, and some record labels have graphic designers on staff to handle these responsibilities in-house.
Training in Cover Art Design:
Education in graphic design is the usual path into designing album cover art. You need familiarity with graphic design software programs and the basics of design. You'll also need to learn how to communicate properly with printers about colors, paper, and other facets of your final design so that the printing comes out as everyone envisioned it. Obviously, you need some creative ability and familiarity with music is a must - most genres have a typical "feel" for the find of cover art they use, and you should be able to listen to music and come up with a design that compliments it.
Making Money Designing Album Cover Art:
Unlike some other jobs in music, pay for designers doesn't change depending on how many copies an album sells. That can be a good thing AND a bad thing. Unless you are a designer on staff at a label, you will be working on a per-campaign basis, charging one flat fee for your work. As you get started, you will likely have to do a few jobs for free to get a foot in the door. The exact pay varies wildly depending on the kinds of labels and artist you work with, and as you work, you'll get a feel for the going rate in your sphere. You can charge different rates depending on the amount of work involved.