Many conspiracies will have a web presence. Searching for them is somewhat easy by using Google.
You may want to consider searching in Private Mode, Incognito, or using the Guest account options on your browser. Further, you may also want to clear your browser's search history after you're done searching.
The web browser DuckDuckGo prides itself on not tracking your search history.
I also recommend checking out Reddit and searching by your conspiracy theory to see if you can find a subreddit page with those who are members or who believe in the conspiracy theory. This will help you recognize the language used within that circle to help you better search the internet for more information about it.