The primary purpose of most first (bachelors) degrees is to learn how to obtain and evaluate information. If you completed your degree more than a few years ago, you are unlikely to have used the full range of resources now available. When you want to learn more about an art movement, an individual artist, or one of their works, the following should provide a good start.
Wikipedia – although its art history coverage is patchy, overall it is the most extensive and comprehensive compilation ever. Be wary that, particularly for less well-known artists, its articles may be compiled from a single source which may not be the most up-to-date or reliable.
Wikimedia Commons – most artists included in Wikipedia also have good collections of images of their work in Wikimedia Commons. These are usually best entered from their Wikipedia entry, although sometimes you have to chase around through less complete galleries before you get to the folders of images.
Heilbrunn Timeline of Art History – superb chronology, essays, and examples provided free by the Metropolitan Museum of Art.
Individual Museums and Galleries – locate some of the artist’s works, and visit the websites of the museums and galleries which hold them; this is helped by using ArtCyclopedia (below) to do the chasing for you. Many will not only have detailed information about that work, but biographic summaries, and you may even chance on a recent exhibition, free book, or more. The larger and public galleries are usually the best for this, but French resources are often surprisingly limited. Most US sites allow non-commercial use of images, but many European sites are still more difficult in this respect.
ArtCyclopedia – lists well-known works with links to museum and gallery coverage, and to their own search facilities. Excellent for tracking down works in major collections, and as a gateway to individual search facilities.
ARC, the Art Renewal Center – a huge collection of mainly non-modern oil paintings. Requires a free account, encourages paid-for membership.
Search engines such as Google – these can turn up excellent sites, but you must be very careful with your search terms, or you will just end up with a vast list of vendors of painted copies or prints.
This blog’s Painting Topics page.
The Burlington Magazine looks very expensive, but is worth every last penny. If you can possibly afford a subscription, pay that bit more to get full access to its amazing archives, going back over a century. It is unique, and is now run by a not-for-profit organisation. A quick search in its archives can save you a great deal of work elsewhere. Its archives are also accessible through JSTOR (below).
British Art Studies is a recent online, open-access (i.e. free to use) peer-reviewed journal covering the area, and looks extremely promising.
The Art Newspaper is best for news about current art, but does cover historical matters too, and is good at topical exhibitions and other news. Consider subscribing, which not only provides you with a monthly printed copy, but gives you free access to full content online too, with iOS apps, etc. There is also The Art Tribune, which carries news, reviews, etc.
Online catalogues raisonnés – there is a growing number of these, listed here.
Christopher Witcombe’s Art History Resources – an extensive list of resources.
JSTOR and academic search engines have in the past been confined to those in academic institutions. However you may well be able to obtain access through your alumnus organisation if you are a graduate. They can search a vast range of publications, including the superb Burlington Magazine, giving you access to PDF copies of papers for many decades, sometimes centuries. Learn to use their search engine and its advanced options to get the best out of them, or like Google you can easily get overwhelmed by useless hits.
Libraries – the most valuable and coherent accounts of art history are still normally those found in books, few of which are published electronically (Kindle, iTunes). Membership and reading facilities at a good library, preferably one supporting a university with a history of art department, is invaluable.
If you have other resources which you wish to share, please add them as a comment.