Many conspiracies will have a web presence. Searching for them is somewhat easy by using Google. Using Google can be a little scary in that your browser will "track" you.
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.
Please feel free to use one of the public computers in the library as well.
Both Twitter and Facebook are good places to search for your conspiracy theory. Does your conspiracy theory group have an account?
Search YouTube for your conspiracy theory, conspiracy organizations, or people involved in your conspiracy. You might find some videos from your conspiracy theories here.
Redditt is a large discussion forum on any topic you can think of including conspiracy theories. It is not advised to engage with other Redditt users while conduction your research.
You may want to use this helpful tool when evaluating the information you find on the internet: