You would just take a screenshot. It doesn't matter though, since it can be faked pretty easily.
Your best bet will be to do a video with Camtasia (not free but on TPB) or Camstudio (Free but not as good), log into your account and show your payments. You must do this LIVE, meaning from the beginning to the end. You can change your password after. This is pretty much the only way that has any cred.
As far as teaching your method to people, idk if there's that much to teach. This is a research gig. You either know the stuff off the top of your head, or you know some Google-fu. That's it. End of story.
Yahoo! Answers, blog search ,etc.
Rinse and repeat. There's all kinds of blackhat methods that one could use as shortcuts that motivated people can find on this forum for free.
Plus, since you are dealing with highschool and college kids who obviously don't have a great grasp on the subject matter, it's probably pretty easy to BS a lot of it, or just rehash what's already online that they were too lazy to search for.
Outsourcing is also an option if the pay is high enough and you are confident that the assignment won't get sniped.
I also agree with Manny that this is a pre-sell thread, and maybe should be closed.