The (accepted and legal) "norm" these days is to post an author pre-print in an institutional open-access repository - check out "green open access" (versus gold open access).
It's not ideal though, but search engines like Google Scholar are good at finding the open-access versions of paywalled academic works and linking to the PDF of them.
Yes - for my doctorate, I wrote several papers, and as a condition of my (public & private) funding they had to be made available publicly.
What I found was that the actual _content_ is served by the university - free for all etc, but any typsetting, editing and formatting became the publisher's property. Yeah sounds daft, but, well, you can get all my papers either directly from the university (via a centralised UK catalogue that Google has managed to link quite nicely) or pay £20+ a shot to Elsevier for the same thing. (Maybe it's different? Looks better? A nicer font? I honestly don't know, but I'm pretty sure the results and stuff are identical, would be quite funny if they weren't)
Might seem pedantic but it's important to be precise: presumably you mean freely available? Publishing makes something publicly available by definition.
This is the "norm" in STEM fields, but not so much in the humanities yet, and I would suspect that some for-profit journals would reject publication of your article if they knew you were already providing a pre-print and so wouldn’t really be respecting the post-publication embargo.
It's not ideal though, but search engines like Google Scholar are good at finding the open-access versions of paywalled academic works and linking to the PDF of them.