I started by just turning off notifications for anything that isn't needed for important people (eg: friends and family) to reach me. I got rid of most social media[0] a little while after that. Another thing I did when I still used a smartphone was remove all the apps from my home screen. At least on iOS, notification badges don't appear in their slide-out app tray thing. For quick access to essentials I used an app that provides a widget for hyperlink like launching of apps

[0]HN, Reddit, and Tumblr are the exceptions for me. I have notifications off and those platforms tend to invite more nuanced discussions and be less distracting over all