My iPhone screen is blank how can I backup my phone?

You can't if your iPhone is defective.

Try -> Restart your iPhone, iPad, or iPod touch - Apple Support

If no joy, make a genius bar appointment with Apple for an evaluation.

They have diagnostic tools and can tell you what options you have.

If your phone isn't working, it's a bit late to back it up now... You have to do that before something goes wrong.