Greeting your R.H.
It all depends on what type of camera you are using.
A webcam often has a small red light to indicate it is on. If so, it might help if you regularly turn it on and off while the birds are in the box they will soon become used to it. This is wired to a computer so can be activate remotely (via your computer).
There are free programs available on the Net that will instruct your webcam to take a picture every minute, 10 minutes, hour or whatever you set it too. Ofcourse, you'll need to leave your computer on while this is going on. Through the same program you can also record actual video clips, say of the birds being fed.
Hope this helps.