Before you even read a source, open another browser tab and Google the website, author, publisher, or organization. Skim through the first page or two of results. If there's a Wikipedia article about the person or organization, skim through that.
This is a fast way to find out authority: whether other people respect the source. If the person or organization is controversial, you will likely discover this through a simple Google search.
Depending on your project, you might still wish to use a controversial or biased source, but you definitely want to know your source is biased or controversial when you use it!