Utilize resources available through your undergraduate university. Visit the pre-medical studies department and talk with your pre-med advisor about options for good clinical experience. Your advisor can often refer you to a good program or helpful hospital or clinic that allows student volunteers.
Visit your personal doctors and contact medical clinics and hospital human resources departments. Explain the type of clinical experience you're looking for and find out what the requirements are for students like you to gain experience.
Consider a job. You can get very good clinical experience as a volunteer, but for hands-on learning, a job in the medical profession is best. As a student, you might not have a lot of free time, but getting certified to be a nurse's assistant or emergency medical technician doesn't take long and the clinical experience you'll receive is invaluable, not to mention very impressive to medical schools.
Look for something long-term. Shadowing a physician for one day is great, but it's not the only clinical experience you should have when applying to medical school. Really good clinical experience will put you in the environment for at least several months, if not a few years.