How do people create website where they have a screen shot inside a phone image?

They are done by taking a screen shot of your app, and then placing that inside of a device PSD (Photoshop file) template which you can find by just Googling for "device name PSD" - for instance here is a iPhone 5 PSD template.

Placeit will do it for you. Pretty slick. And free.

You could also pay a designer about $5 to insert a screen shot (that's what we did).