Away
Here's the method. It has two parts, and this is the first. When someone is talking to you, the phone is away, which means out of your hands and out of your sight.
The definition matters, because the natural compromise is the phone face down on the table, and that isn't away. The restaurant study's phone-out condition was phones on the table, and that's where the distraction came from. Misra's observers counted a phone on the table as present, and the conversations with a phone on the table were rated worse. Face down, the phone still buzzes against the wood, still lights the edge, and still holds the thread that Ward's experiments found even a silent phone holds. Away means a pocket, a bag, a drawer, the hall, the kitchen counter when you're in the living room. Somewhere your hand can't go without your legs.
Where it goes depends on the conversation. At the table, the phone isn't at the table. Yours, in a bag or the hall, before the food's put down. This is the easiest one to make into a fixed rule because meals have a start. On the sofa in the evening, the phone lives somewhere that isn't the arm of the sofa. If the earlier book The phone can wait has already given your phone a home, it's the same place. At bedtime with a child, it doesn't come into the room. In the car with a child, it's in the glove box, which is also where a later book on driving will want it. On a walk or in a cafe with a friend, it's in the pocket or bag, and it stays there.
What about the person walking into a room where you're already on the phone? That's the second part of the method, in chapter 18. This part is for the conversations you can see coming.
You'll notice the tug more, not less, in the first days of doing this, because the phone was answering it before you'd felt it. That's fine. It's the habit becoming visible, and a visible habit is one you can not do. And you'll notice something else within a week. Conversations get longer. Not because anyone decided to talk more. Because the drop stopped happening, and stories that were being cut short started reaching their ends.