What can a non-researcher/academic do to promote open access?
Some thoughts:


Write their representatives in government. Encourage them to support open access mandates for publicly funded science.
Write the authors of open access papers they do read, and thank them for making their work open access. Positive feedback, even if it's not career-altering, is always nice.
Give to their local university/alma mater/etc.'s capital campaign, specifically to support funding to help cover open access charges for projects that don't have enough funding to pay for those fees themselves (often grad student/postdoc projects).