GoKawiilDo Not Disturb and Focus live in your iPhone's Control Center, accessible by swiping down from the top-right corner of your screen. If you're still rocking an iPhone with a Home button, slide up from the bottom instead. Tap the Focus button and you'll see every available option laid out: classic Do Not Disturb, plus Personal, Work and Sleep. To tweak a specific mode, tap the three dots, then Settings.
If you've never used a Focus before, you'll need to set it up first. That's what makes this feature so powerful: in its settings (Settings > Focus), you can choose which apps and people are allowed to notify you when a mode is on. Let's say in the Work Focus, you only allow notifications from apps like Slack and Mail, while all others are silenced. The same goes for people; it's in your control whether calls or messages from specific contacts notify you.
To set these up, tap People or Apps while inside a Focus's options. You can choose to Allow or Silence Notifications From the list you created — whichever makes more sense for that Focus. Under Apps, be sure to enable Time Sensitive Notifications so you still receive important alerts like reminders, alarms or calendar events. You can also customize a Focus mode by applying Filters and Smart Activation. It's definitely worth taking the time to check out all the available options, given what a great productivity tool Focus is.
As you may notice, Do Not Disturb is its own Focus, meaning it's customizable like the rest. You might wish to allow alerts from your spouse even in Do Not Disturb, perhaps.