If you want to become a payroll clerk, you need to find some combination of skills and training in order to get a company to hire you. An accounting background would be helpful. If you haven’t had any accounting classes in high school, you’ll probably want to take an introductory financial accounting class and a class on payroll management if one is available at a nearby college or adult education program.
In any case, there are multiple ways to approach your goal of becoming a payroll clerk. A two-year Associate’s degree in accounting would help, but a Bachelor’s degree would probably over qualify you for a clerk position.
A job doing payroll as part of a bookkeeping job for a smaller company might be an avenue into a payroll clerk position for a larger company. That way, you will get experience working with a payroll system and have the credentials to move into a pure payroll position. It might not get you into positions that are looking for pure payroll experience, but if they are looking for payroll familiarity, a bookkeeping position might do the trick.
Getting practice on key payroll software packages and accounting packages in general, would be good. Many temp agencies will let you train on software packages so that you can serve their clients better. You might want to get a foot in the door in some other capacity with an agency and then uses their tutorial packages to learn the various systems in play.
Temps jobs in payroll are another route in. If you master a payroll package through an agency’s tutorial system, they may give you a shot at doing a payroll assignment. If the company you are assigned to likes you, you may get a long-term job offer from them, but even if they don’t, you now have payroll experience to put on your resume and have fired a “shot in anger” using the payroll package.
Getting a clerical job within a large company, especially one involving accounting, such as accounts payable or accounts receivable, might be a backdoor into an a payroll job. Once you show your worth in a company, you can apply to internal payroll positions within the company. For instance, if you got a job as a billing clerk at a hospital and had either the accounting coursework and/or the software background, you could apply for a payroll position at the hospital and have your boss in billing vouch for your work ethic.
Finally, networking always helps, for many positions aren’t posted formally. If you are in a company, get to know the accounting and payroll people and let them know in a non-pushy manner that you’d be interested in moving over to payroll if the need arises. If you've met some respected professors while pursuing your education in accounting, you can also approach them for recommendations.