I am addicted to my phone, like most people.
If you want to understand the underlying effects and mecanisms of how smartphones and apps are designed to be addictive, I invite you to read this article: How Technology is Hijacking Your Mind.
What I did to overcome this addiction are simple steps:
Remove all non-important and non-urgent notifications.
Do you need to know right know that you are receiving this email? That this guy liked your photo? I am not sure at all. Let's face it together and remove those unneeded notifications.
I just have notifications enabled for phone calls and messages. The only exception is for mail, but I only let the badge icon, no sound, no vibration, no preview: I don't need to know instantly about it, it's a mail. How often do you check your real mail box anyway? Put that in perspective.
Remove all apps that are not necessary. Seriously I just have Whatsapp installed.
Make your phone a boring phone
For this extra step, your battery will thank you. I did this for a moment and it's quite funny. Go to Settings > General > Accessibility > Greyscale. Yes. Do it. The strange effect is when you turn the colors back on after a few days, and you notice how sweet they are to your eyes.
More time, a better sleep pattern, more disk space for photos and music, and overall a better battery life.
Another option is to take a dumb phone like an old nokia, but your life will be difficult quite quickly I assure you.