How to backup and restore from black screened Nexus 6

I have a Motorola Nexus 6. I dropped it the other day and shattered the screen, also I think cracking the LCD, because now the screen is almost all black and looks like it has ink spilled on it. Any way, I can't see hardly anything on it. I can get a replacement, but don't know how to get all of my app data, pictures, contacts, etc. off of it when I can't see anything on the screen. I would like to backup everything on my phone including app files, like password apps and bill paying apps, etc. and put it on a new phone, and have it be exactly the same. Also, is there something I could use to wipe all of my personal data from the broken phone, before sending it back to the replacement company, since I can't see anything on the screen?

thanks,

Doug