The least coercive way to do it is probably by making areas closer to the city center worse for driving — narrow roads, no parking, etc — and better for walking and biking. Then people will naturally sort themselves based on their preferences. The problem being that establishing the needed urban environment is itself a political struggle.
I never drive to London because a train will get me there faster, and I can rely public transport to get me to almost anywhere I want to get to. It can definitely be useful to have a car in the suburbs but not enough to be worth the trouble of driving one there.
The difficulty of parking and driving around the city centre is a deterrent, but to me it is secondary to the positive factors.
I do like pedestrianised areas, because they feel safe and clean. The main danger remaining is the cyclists of the "get out of my say" type, especially couriers and the like.
How so? We've built huge amounts of infrastructure (parking being the obvious one) to explicitly enable people to have cars in city centers- stop doing that and my gut (scientific, I know!) says that'll get you most of the way there.
Strongly feel this acceptance will be difficult to actualize sans coercion.