Check for Previous Work
Look around to see if someone else has already fact-checked the claim or provided a synthesis of research.
Go Upstream
Go "upstream" to the source of the claim. Most web content is not original. Get to the original source to understand the trustworthiness of the information.
Read Laterally
Once you get to the source, read what others have to say about the source (publication, author, content, etc). The truth is in the network. To do this, open a new tab in your browser, and Google the information/source/organization.
Circle Back
If you hit dead ends or start going down a rabbit hole, back up and start over knowing what you know now.