Tough one. I'm not sure there's a universal answer, it definitely depends on the person and the said addictions.
As far as I was concerned, it was antidepressants and marijuana. As far as antidepressants go, since I was against going into a rehab center and I knew for sure I was gonna go through some Trainspotting kind of shit, I just isolated myself in a friend's flat while they were on vacation, around early September. It was the hardest fight I've ever been in. Going cold turkey on meds is a dangerous process, it can fuck you up forever, you have to be SURE you want to do this.
Miraculously, I made it. Let me tell you I was pretty fucking proud of myself. The physical symptoms of meds withdrawal are straight up torturous. It's not just being a bit more nervous, it is downright physical masochism.
In the process, I tried to quit weed as well, and I held it for a few days, but a couple of events just threw me back in it. Also, even though I had beat meds, I was still feeling depressed every now and then. And then, a couple of weeks ago, I don't know man, I just woke up, and it was gone. I felt great. I felt positive again. I could finally enjoy everything that was around me. Music, movies, people, activities. Then, quitting weed was a piece of cake.