A couple months ago I did a 1 day screen fast, no phone and no laptop. It was a great experience, and shows you just how much the constant communion with devices affects us. My mind felt...different. Less jumpy. Overall it was a huge positive, and when you tell people about it they're amazed, it's such an uncommon thing to do. I did things that had been on my to-do list for a long time.
After that, I thought I'd do it once a week, but ended up doing it only a couple times since then. The problem is, going without your phone nowadays equals going without telephones, telephone books, maps, address books, calendars, encyclopedias, cookbooks, regular books, etc. Things you need for everyday life.
It helps to prepare ahead of time. Go through your to-do list, and write things down on paper. Longer term, I'd like to start the process of becoming more independent of online services. For instance, I was using a online note-organizing app. I switched to text files, it wasn't that difficult.