Open access (OA) has come to symbolize the revolution in scholarly publishing, though the revolution goes much deeper and is much wider. Fundamentally, open access means what it says, access to scholarly works in the open -- without paywalls and with a license for reuse. This concept has been around for well over 20 years and had its roots in what became known as the crisis in scholarly publishing - the double-digit inflation in the prices of serials over a decade or so that threatened to completely upend the relationship between books and journals in collection development. At one time many thought moving scholars' research results to freely accessible institutional or disciplinary servers would ultimately bring down the prices of journals, if not eliminate the need for them altogether. This has turned out to be illusory. Publishers have us over a barrel for the most part, and they know it and act accordingly. It is ironic that it's our own content they use to reap their generous profit margins from us, but we're the ones who willingly give over the content and then fork over the money to buy it back. What do we expect normal ordinary for-profit publishers to do? They owe allegiance to their shareholders. Well, enough crying over the spilt milk.
Open access is gaining traction; there are advances on legal fronts; and business models are evolving to acknowledge the inevitability of OA. It only seems a matter of time before the opportunity will be a reality for every single scholar to have his or her work available freely on the web. But that same work will in many cases still be published in exactly the same journal that the scholar might have published in 20 years ago, though it will have gone through a couple of name changes and be owned by one of the 2 or 3 publishers left in the field. Consolidations have been pro forma. This is not to say that there won't be grand departures from the norm also, new modes of scholarly communication and publication, but I think that we'll have quite traditional publishing with us, though not alone on the stage as it is today, for a long time.
As content stops being king, services are likely to take its place. Publishers will compete for subscription dollars based not on what articles they allow you to make available, but on what services they allow you to offer built on the corpus of freely available materials. It will be interesting to see whether competition in services will be more robust (i.e. affecting prices) than competition in scholarly articles is. That was always a big part of the problem with content as king: articles were not fungible. One journal's content could never substitute for another's. Articles are unique, as are their authors. But services are easier to duplicate, except to the degree they are based on patents, but let's not get off on that tangent.
Open access resources
There are so many sources for information on this topic. If you just want to know the basics, the first stop is SPARC. If you really want to dig into resources, I recommend the Open Access Directory. And, if you'd like more personalized information, your library is probably your best bet - they likely have a librarian or librarians who can talk with you about OA. Many libraries offer services to their institutions' faculty to help them take advantage of options their publishers give them to archive their pre- and post-prints, and to negotiate modifications to their contracts that allow for archiving if the publisher does not allow it by policy. You can determine what most publishers' policies are regarding open access at Sherpa's RoMeo site.
Public access requirements
Many funding agencies are now requiring grantees to share the results of their research - both scholarly articles and data. The NIH has required grant recipients to share their articles via PubMed Central since 2008. Since that time, many federal funding agencies have come up with their own data and publication sharing plans. SPARC has a really great comparison tool that looks at funding agency requirements for data. It's quite likely that researchers applying for grants will have some sort of sharing requirement they need to comply with. Librarians on most college campuses are available to assist researchers that have questions about these requirements.