how do i back up my iphone if my screen is broken

It's too late for that. You need to back up before it fails, not after.

If the iPhone was backed up on a computer running iTunes, and it is not disabled connect to that computer and see if it will allow you to backup again.

If it has not been backed up previously, it cannot be backed up now if you cannot use the screen. You will need to take it to an Apple store genius bar to see about having the screen replaced.