Contact the volunteer coordinator at any nearby hospital or clinic or nursing home where you wish to volunteer and ask to fill out an application. The clinical site will usually require that you take some training classes and provide your immunization records before you can work with patients. (As a FYI, you’ll need an up-to-date flu shot.) The volunteer site will also usually ask you to provide one or more character references as part of your application.
If you want to be an EMT (or CNA or MA), you must hold a valid state license. To get a license, you must first take and pass the training classes and then pass a the state or national licensing exam. You can find EMT, CNA and MA classes at your local community college or at for-profit institutions like Pima Medical Institute.