How do I lock my screen for backup?

If you are using the Backup Now option for iCloud Backup, you do not lock the screen. For the phone to automatically backup to iCloud while charging, it does need to be locked. You can do that by pressing the right side button or do what I do and let it lock itself based on the time you have chosen in Settings > Display & Brightness > Auto-Lock.

You unlock it the same way as always -- via Touch ID or your passcode.

The screen locks when you press the side button. It unlocks when you hold your finger on the HOME button. It will also lock if you leave the phone idle for longer than the auto-lock setting.