How do I backup my iPhone 12 if it won’t turn on?

You can connect it to your computer to see if you can backup it that way. There is no guarantee that that will work tho. But in general, you will need to backup on a regular basis, not only when your iPhone is broken

See this instructions for further reference about backing up via a computer

Back up iPhone using your Mac

1. Connect iPhone and your computer with a cable.
2. In the Finder sidebar on your Mac, select your iPhone.
3. To use the Finder to back up iPhone, macOS 10.15 or later is required. With earlier versions of macOS, use iTunes to back up iPhone.
4. At the top of the Finder window, click General.
5. Select “Back up all of the data on your iPhone to this Mac.”
6. To encrypt your backup data and protect it with a password, select “Encrypt local backup.”
7. Click Back Up Now.

Note: You can also connect iPhone to your computer wirelessly if you set up syncing over Wi-Fi.

Back up iPhone using your Windows PC

1. Connect iPhone and your computer with a cable.
2. In the iTunes app on your PC, click the iPhone button near the top left of the iTunes window.
3. Click Summary.
4. Click Back Up Now (below Backups).
5. To encrypt your backups, select “Encrypt local backup,” type a password, then click Set Password.

To see the backups stored on your computer, choose Edit > Preferences, then click Devices. Encrypted backups have a lock icon in the list of backups.

Note: You can also connect iPhone to your computer wirelessly if you set up syncing over Wi-Fi.

SisKay931 wrote:

My iPhone 12 will not turn on. I have an appointment with an Apple Store. They ask that you back up your phone before the appointment. How do I do this if I can’t turn it on?

You don’t. It’s too late for that.