how do i backup my phone with a broken not working screen?

The time to do a back-up is BEFORE the device is broken. If you were using iCloud, you might find some things backed up there, but otherwise, without a working back-up, you will be unable to restore the device.

If you have automatic iCloud backup on and autoconnect to known wifi networks, plug it into power and leave it sit for 24 hours.

If you didn't set that up, you don't back it up.