Finding information online today is hardly challenging. The challenge is to find high quality information that meets your specific needs. Be discriminating! Here are some questions you should ask yourself when you are sifting through your search results, looking for gems of information.
Authority - Who wrote it or who is responsible for it? Why should I care what they think?
Look for who wrote the website, or the larger organization responsible for it if there is no individual author.
Look for an About Me or About Us link. If the creator(s) want to be taken seriously, they need to make it obvious to the reader who they are and their credentials. (Though sometimes they think they are well known enough to not bother, or to bury such info. Try finding "about us" info on the New York Times's site.)
Want to know more about the larger organization? Google the name. If there isn't a Wikipedia entry about the organization, they aren't prominent. This will work for some individuals as well, if they are well-known enough.
It is tempting to look at the URL of the website and make assumptions based on whether it is a .com or .org or .edu. But the truth is that anyone can purchase a .com or .org, and the .edu is not limited to professors or departments. Some schools give all of their students space to create their own websites which would have a .edu domain. The only domains that are truly "locked down" are .gov for state and federal government agencies and .mil for US military websites.
Evidence - What evidence does the source use to back up assertions? Is the information sound? How does it compare with other sources?
This is the most important criterion to judge your source. But it is the one that takes the most time, because you have to know enough about your issue to judge the soundness.
Comprehensiveness - How complete and balanced is the analysis?
Some sources will be relevant and useful, but do not give the reader a complete picture in their analysis. The more comprehensive sources (and therefore the lengthiest!) will be especially useful at the beginning of your research, when you are still absorbing as much as possible.
Purpose - Why is this available online for free?
If you can answer this question, you have successfully examined the authority and credibility of the site. Libraries specialize in collecting information that costs money. But there are a lot of people and organizations who want to freely share their expertise and knowledge. They may have an agenda, of course, but that's true with the information you get from the library's databases as well.