It’s highly unlikely you’re going to find exactly what you’re looking for with a single search (and if you do, the information is quite possibly suspect). Be prepared to wade through a lot of information looking for the right information.
The information you need will not always come predigested on someone’s webpage. Be willing to read tables of contents and download articles and comb through entries in a database. It may seem to take longer, but fruitlessly running web searches that don’t turn up any useful results takes time as well, and it’s frustrating and annoying.
Build on what you learn
Say you’re researching Avicenna and you learn another way to spell his name is “Ibn Sīnā”. Now you can search for both versions and probably turn up more results. If you come to the end of an article or a webpage and there’s a Works Cited section, try looking up some of the sources the original writer used. Each search you make doesn’t need to be a blank slate.
Think outside the (search engine) box
Most of us just pull up Google when we need something, and if you’re looking for something superficial (“What year did the Opium Wars begin?”), it’ll probably fit the bill. But if you’re looking for specialized information (“Was there a specific name for the bag an American Civil War doctor carried medical equipment in?”), you’re going to want to search in a more targeted way.
Academic libraries’ subject-specific pages. Sure, some of the resources will be unavailable to non-students, but some of them are available to everyone. Subject librarians have already done some of the legwork for you; use it to your advantage. For example, I found the African e-journals project via the History: Africa subject page at UW Libraries.
National libraries. Try searching for “national library” and the country you’re interested in, then dig through the site for freely available materials. For instance, I found a a lot of freely available digitized journals relating to Welsh history and culture via the National Library of Wales.
National archives. These often have considerable digital collections. Find them the same way you’d find national libraries. Some examples:
Evaluate like a mofo
We all know just because something is on the internet doesn’t make it true. For all but the most superficial inquiries, be very wary of materials online without citations.
Some well-cited resources:
Gatehouse Gazetteer – A database of medieval structures in England and Wales
Food Timeline – Details the first recorded appearance of different foods worldwide
The Old Bailey Online – Legal history in the UK
Find your people
Most of the best resources I’ve found have come from Twitter. I follow historians, independent scholars, librarians, medievalists, and just about every stripe of history geek there is. They tweet some really great stuff.
Being connected to people with similar interests on all types of social media will often bring you resources that won’t turn up on a standard Google search. Don’t forget to retweet/favorite/comment or otherwise be in touch to let them know you appreciate their efforts!
Leverage your existing resources
Your public library most likely has access to databases and resources you can access from home with your library card. Also, don’t be afraid to ask the librarians for help or advice. Believe me, they will love answering a question that doesn’t involve the location of the bathroom or what’s wrong with the printer.
If you graduated from college, your alumni association may have arrangements to provide alums with access to resources like JSTOR. And even if you didn’t, public universities typically provide access to their online resources to anyone who comes physically to campus; if you live near one, ask the librarians about the policy on guest use.
Do the right thing
There will come a time when you encounter a great resource that has been uploaded without the creator’s knowledge and/or consent, but there are plenty of ways to access content without engaging in piracy. Please explore those options so the creator will be able to continue to produce content you find useful. In particular, your local library wants to help connect you with the information you need. It may take longer, but it benefits everyone in the long run.
Other starting points:
Archive.org – An open-source clearinghouse of primary and secondary sources
Bamboo DiRT – Not a information site per se, but free tools to organize and efficiently use the information you gather.
Directory of Open Access Journals – A searchable collection of peer-reviewed journals available without a subscription
Hathi Trust – A digital library that provides access to scanned books and articles