In this materials component, you can find an overview of the procedure (both as word and pdf document), the stimuli as provided by the original authors (see their osf project), and an exemplary study design that can be used in lab.js.
[lab.js][1] is a software to create online studies. It is based on javascript, but offers a visual programming interfcae (builder). You can simply go to https://labjs.felixhenninger.com/ to use the software. Open the fakenewscrep.study.json file and adjust it to your needs. You can deploy the study so that your participants can find it online via different ways, the easiest is probably [open-lab][2].
Of course, you don't have to use lab.js or open-lab, you can also use qualtrics or any other program to run online studies.
[1]: http://lab.js.org/
[2]: https://www.open-lab.online/