There are two main options:
Gold Open Access Publishing
This is when the journal you publish in makes digital content freely available immediately upon publication.
This can be done in two ways:
Open access journals generally publish your work under a copyright licence, rather than an assignment of copyright.
This is the difference between you retaining copyright ownership of your work and the journal owning your publication.
Green Open Access Publishing
This is when you continue to publish in traditional subscription-based journals, however the publisher allows you to deposit (self-archive) a digital copy of the article manuscript online.
You will usually be allowed to deposit the author’s final manuscript in either a subject-based or institutional repository (ie. UC’s Research Repository), or by posting the article to your personal website.
Many authors prefer the green option because it allows you to continue publishing with well-established journals in your field.
These databases include many open access journals; look for the words 'Open Access' in your search results, or use the Open Access filter on the left menu of the search results page. They also shows if the paper has an open access version available via the web e.g. from a university repository.