How do I know when my phone has updated?

If you meant, the iOS (operating system software of the phone), then goto Settings > General > Software Update, it will display what version of iOS you're on and whether there is an update for your phone. You can also choose whether you want to Customize Automatic Updates for your phone on this page.

And if you meant the updates for your apps on the phone, then launch the App Store app on your phone. At the top right, click on your personal icon to navigate to the Account page. On this page, it will list apps that have On the Next screen, tap on Don’t Allow to prevent deleting of Apps on your iPhone. and also list apps that have updates pending.

Hope this helps!

Do you mean when an update has been completed? There is usually a short message that the phone is up to date when it is done installing.