Follow someone with a video camera, wait till they record something, shoot them with a pistol/rifle/shotgun/assault rifle/arrow/crossbow or strike them with an ax/machete/scythe/cane cutter, take their video camera and say you found it!
You basically have two stories playing out--(1) what happens in the "found footage" and (2) what happens with the people who find it. I want to emphasize again, use note cards so you can keep track of the events as they play out. Play out (2) linearly. Use it as the background for orienting the audience. Story (1) can be linear or non-linear AFTER you've written out the story in a linear form. [Basically you reorganize the cards and draw parallels or contrasts to events in the "reality" (2).] Writing solid narratives for (1) and (2) is important.
Maybe instead of asking on this forum, you actually think carefully about your question first... I'm getting deja vu here.
The answer will then come to you...
ANSWER: Read some good produced found footage scripts.
Then you could ask a better question: Where can I find some good found footage scripts. We can obviously answer that much easier than: 'How do you write a found-footage movie?'