How do you crop one person or thing from a video and put it into another video?

I was watching videos on YouTube like this one and I want to know how to do it… And if there's any iPhone apps to help me, I don't have access to a computer right now

Yeah, no. You NEED a computer to be able to pull off video editing like that.

It's too complicated to do on a smartphone.
video editing takes a ton of processing power, and more powerful programs than you can get on a phone.