Getting surveillance camera footage streamed to phone

I am studying computer programming, but I feel that at school we are doing only stuff that work on a computer without having any connection to the outside world and it isn't all that interesting, so I gave myself a challenge. I want to make a program that streams footage from a surveillance camera to a phone. It seems a bit of a long shot, but I want to try. The thing is that, as I said, at school we are doing pretty basic stuff and with a project like this I have no idea how to even begin. A simple Google search didn't help at all.

I know how mobile apps are made, but I have no idea how to connect such devices.

Any ideas?