Start by volunteering in a hospital. Test whether this is something real or just something out of the blue. It will also show interest when you apply to postbac programs.
Then try speaking with doctors. I asked my primary care doctor if he would do an "informational interview" with me. He agreed readily and was so, so helpful.
Decide what type of postbac program you are looking for. Other threads can explain the different types better than I can. I went to Bryn Mawr, which is a highly, structured, intensive, full-time program. It has a v. high rate of success but is also expensive. Peer programs include Goucher and Columbia.